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2014
Analysis of a Fuel Cell Combustor in a Solid Oxide Fuel Cell Hybrid Analysis of a Fuel Cell Combustor in a Solid Oxide Fuel Cell Hybrid
Gas Turbine Power System for Aerospace Application Gas Turbine Power System for Aerospace Application
Ryan R. Sinnamon Wright State University
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ANALYSIS OF A FUEL CELL COMBUSTOR IN A SOLID OXIDE FUEL CELL
HYBRID GAS TURBINE POWER SYSTEM FOR AEROSPACE APPLICATION
A thesis submitted in partial fulfillment
of the requirements for the degree of
Master of Science in Engineering
By
RYAN RUSSELL SINNAMON
B.S., Wright State University, 2012
2014
Wright State University
WRIGHT STATE UNIVERSITY
GRADUATE SCHOOL
April 30, 2014
I HEREBY RECOMMEND THAT THE THESIS PREPARED UNDER MY
SUPERVISION BY Ryan Russell Sinnamon ENTITLED Analysis of a Fuel Cell
Combustor in a Solid Oxide Fuel Cell Hybrid Gas Turbine Power System for Aerospace
Application BE ACCEPTED IN PARTIAL FULFILLMENT OF THE
REQUIREMENTS FOR THE DEGREE OF Master of Science in Engineering.
Committee on
Final Examination
Scott Thomas, Ph.D.
Hong Huang, Ph.D.
Robert E.W. Fyffe, Ph.D.
Vice President for Research and
Dean of the Graduate School
Rory A. Roberts, Ph.D.
Thesis Director
George Huang, Ph.D.
Chair
Department of Mechanical and
Materials Engineering
College of Engineering and
Computer Science
iii
ABSTRACT
Sinnamon, Ryan Russell. M.S.Egr., Wright State University, 2014.
Analysis of a Fuel Cell Combustor in a Solid Oxide Fuel Cell Hybrid Power System for
Aerospace Application.
Over the last few years, fuel cell technology has significantly advanced and has
become a mode of clean power generation for many engineering applications. Currently
the dominant application for fuel cell technology is with stationary power generation.
Very little has been published for applications on mobile platforms, such as unmanned
aerial vehicles. With unmanned aerial vehicles being used more frequently for national
defense and reconnaissance, there is a need for a more efficiency, longer endurance
power system that can support the increased electrical loads onboard. It has already been
proven by others that fuel cell gas turbine hybrid systems can achieve higher system
efficiencies at maximum power. The integration of a solid oxide fuel cell combustor with
a gas turbine engine has the potential to significantly increase system efficiency at off-
design conditions and have a higher energy density compared to traditional heat based
systems. This results in abilities to support larger onboard electrical loads and longer
mission durations. The majority of unmanned air vehicle mission time is spent during
loiter, at part load operation. Increasing part load efficiency significantly increases
mission duration and decreases operational costs. These hybrid systems can potentially
have lower power degradation at higher altitudes compared to traditional heat based
propulsion systems. The purpose of this research was to analyze the performance of a
solid oxide fuel cell combustor hybrid gas turbine power system at design and off-design
operating conditions at various altitudes. A system level MATLAB/Simulink model has
iv
been created to analyze the performance of such a system. The hybrid propulsion system
was modeled as an anode-supported solid oxide fuel cell integrated with a commercially-
available gas turbine engine used for remote control aircraft. The design point operation
of the system was for maximum power at sea-level. A steady-state part load performance
analysis was conducted for various loads ranging from 10 ≤ L ≤ 100 percent design load
at varying altitudes ranging from 0 ≤ Y ≤ 20,000 feet. This analysis was conducted for
four different fuel types: humidified hydrogen, propane, methane, and JP-8 jet fuel. The
analysis showed that maximum system efficiency was achieved at loads of 40 ≤ L ≤ 60
percent design load at each altitude and fuel type. The system utilizing methane fuel,
internally-steam reformed within the fuel cell, proved to have the highest system
efficiency of 46.8 percent (LHV) at a part load of L = 60 percent and an altitude of Y =
20,000 feet.
v
TABLE OF CONTENTS
Page
INTRODUCTION .............................................................................................................. 1
BACKGROUND ................................................................................................................ 7
Solid Oxide Fuel Cells .................................................................................................. 10
MATHEMATICAL MODEL ........................................................................................... 11
Solid Oxide Fuel Cell Model ........................................................................................ 12
SOFC Electrochemistry ................................................................................................ 12
SOFC Polarization Losses ............................................................................................ 15
Activation Polarization ............................................................................................. 15
Ohmic Polarization ................................................................................................... 17
Concentration Polarization........................................................................................ 18
Energy Analysis ............................................................................................................ 20
Combustor Model ......................................................................................................... 22
Gas Turbine Model ....................................................................................................... 22
SOFC Combustor / GT Model ...................................................................................... 24
RESULTS AND DISCUSSION ....................................................................................... 26
Steady-State Part Load Performance Analysis ............................................................. 27
Impact to UAV Performance ........................................................................................ 40
CONCLUSIONS .............................................................................................................. 42
vi
APPENDIX A: MATLAB/SIMULINK MODEL FILES ................................................ 45
APPENDIX B: EFFECTIVE DIFFUSIVITY: LEONARD-JONES POTENTIALS ...... 51
APPENDIX C: SOFC/GT FUEL CHEMISTRY ............................................................. 53
APPENDIX F: SUMMARY OF SOFC/GT MODEL DATA .......................................... 55
REFERENCES ............................................................................................................... 107
vii
LIST OF FIGURES
Page
Figure 1: Anode Supported SOFC Schematic. ................................................................. 10
Figure 2: Traditional Gas Turbine Engine Schematic. ..................................................... 24
Figure 3: SOFC/GT Schematic. ........................................................................................ 25
Figure 4: System Efficiency versus Part Load: (a) Sea-Level; (b) 4,000 ft. ..................... 31
Figure 5: System Efficiency versus Part Load: (a) 8,000 ft; (b) 12,000 ft. ...................... 32
Figure 6: System Efficiency versus Part Load: (a) 16,000 ft; (b) 20,000 ft. .................... 33
Figure 7: Fuel Utilization versus Part Load – CH4 (SR). ................................................. 35
Figure 8: Compressor Mass Flow versus Part Load – CH4 (SR). .................................... 36
Figure 9: Solid Oxide Fuel Cell Voltage versus Part Load – CH4 (SR). ......................... 36
Figure 10: System Efficiency versus Part Load: Methane Steam Reformation. .............. 37
Figure 11: System Efficiency versus Part Load: JP-8 Steam Reformation. ..................... 38
Figure 12: System Efficiency versus Part Load: Humidified Hydrogen. ......................... 38
Figure 13: System Efficiency versus Part Load: Methane Partial Oxidation. .................. 39
Figure 14: System Efficiency versus Part Load: Propane Partial Oxidation. ................... 39
Figure 15: System Efficiency versus Part Load: JP-8 Partial Oxidation. ......................... 40
Figure 16: CH4 (SR) – System Load versus Part Load. ................................................... 56
Figure 17: CH4 (SR) – Fuel Utilization versus Part Load. ............................................... 57
Figure 18: CH4 (SR) – Turbine Inlet Temperature versus Part Load............................... 58
Figure 19: CH4 (SR) – Gas Turbine Shaft Speed versus Part Load. ................................ 59
Figure 20: CH4 (SR) – Compressor Mass Flow Rate versus Part Load. .......................... 60
Figure 21: CH4 (SR) – Solid Oxide Fuel Cell Voltage versus Part Load. ....................... 61
Figure 22: CH4 (SR) – Solid Oxide Fuel Cell Power versus Part Load. .......................... 62
viii
Figure 23: CH4 (SR) – Gas Turbine Power versus Part Load. ......................................... 63
Figure 24: JP8 (SR) – System Load versus Part Load. ..................................................... 64
Figure 25: JP8 (SR) – Fuel Utilization versus Part Load.................................................. 65
Figure 26: JP8 (SR) – Turbine Inlet Temperature versus Part Load. ............................... 66
Figure 27: JP8 (SR) – Gas Turbine Shaft Speed versus Part Load. .................................. 67
Figure 28: JP8 (SR) – Compressor Mass Flow Rate versus Part Load. ........................... 68
Figure 29: JP8 (SR) – Solid Oxide Fuel Cell Voltage versus Part Load. ......................... 69
Figure 30: JP8 (SR) – Solid Oxide Fuel Cell Power versus Part Load............................. 70
Figure 31: JP8 (SR) – Gas Turbine Power versus Part Load. ........................................... 71
Figure 32: H2 – System Load versus Part Load. .............................................................. 72
Figure 33: H2 – Fuel Utilization versus Part Load. .......................................................... 73
Figure 34: H2 – Turbine Inlet Temperature versus Part Load. ......................................... 74
Figure 35: H2 – Gas Turbine Speed versus Part Load. ..................................................... 75
Figure 36: H2 – Compressor Mass Flow Rate versus Part Load. ..................................... 76
Figure 37: H2 – Solid Oxide Fuel Cell Voltage versus Part Load.................................... 77
Figure 38: H2 – Solid Oxide Fuel Cell Power versus Part Load. ..................................... 78
Figure 39: H2 – Gas Turbine Power versus Part Load. .................................................... 79
Figure 40: CH4 (POX) – System Load versus Part Load. ................................................ 80
Figure 41: CH4 (POX) – Fuel Utilization versus Part Load. ............................................ 81
Figure 42: CH4 (POX) – Turbine Inlet Temperature versus Part Load. .......................... 82
Figure 43: CH4 (POX) – Gas Turbine Shaft Speed versus Part Load. ............................. 83
Figure 44: CH4 (POX) – Compressor Mass Flow Rate versus Part Load........................ 84
Figure 45: CH4 (POX) – Solid Oxide Fuel Cell Voltage versus Part Load. .................... 85
ix
Figure 46: CH4 (POX) – Solid Oxide Fuel Cell Power versus Part Load. ....................... 86
Figure 47: CH4 (POX) – Gas Turbine Power versus Part Load. ...................................... 87
Figure 48: C3H8 (POX) – System Load versus Part Load. .............................................. 88
Figure 49: C3H8 (POX) – Fuel Utilization versus Part Load. .......................................... 89
Figure 50: C3H8 (POX) – Turbine Inlet Temperature versus Part Load. ........................ 90
Figure 51: C3H8 (POX) – Gas Turbine Shaft Speed versus Part Load. ........................... 91
Figure 52: C3H8 (POX) – Compressor Mass Flow Rate versus Part Load. .................... 92
Figure 53: C3H8 (POX) – Solid Oxide Fuel Cell Voltage versus Part Load. .................. 93
Figure 54: C3H8 (POX) – Solid Oxide Fuel Cell Power versus Part Load. ..................... 94
Figure 55: C3H8 (POX) – Gas Turbine Power versus Part Load. .................................... 95
Figure 56: JP8 (POX) – System Load versus Part Load. .................................................. 96
Figure 57: JP8 (POX) – Fuel Utilization versus Part Load. ............................................. 97
Figure 58: JP8 (POX) – Turbine Inlet Temperature versus Part Load. ............................ 98
Figure 59: JP8 (POX) – Gas Turbine Shaft Speed versus Part Load................................ 99
Figure 60: JP8 (POX) – Compressor Mass Flow Rate versus Part Load. ...................... 100
Figure 61: JP8 (POX) – Solid Oxide Fuel Cell Voltage versus Part Load. .................... 101
Figure 62: JP8 (POX) – Solid Oxide Fuel Cell Power versus Part Load. ...................... 102
Figure 63: JP8 (POX) – Gas Turbine Power versus Part Load....................................... 103
x
LIST OF TABLES
Page
Table 1: Fuel Cell Characteristics ....................................................................................... 9
Table 2: SOFC Activation Polarization Model Input Parameters .................................... 17
Table 3: SOFC Ohmic Polarization Model Input Parameters .......................................... 18
Table 4: SOFC Concentration Polarization Model Input Parameters. .............................. 19
Table 5: Specific Heat Coefficients for Various Gases. ................................................... 21
Table 6: Gas Turbine Model Input Parameters. ................................................................ 24
Table 7: Fuel Processing - Hydrogen Yield. ..................................................................... 28
Table 8: Maximum System Sizes – Sea-Level at Full Load ............................................. 28
Table 9: Part Load Performance Efficiency Model Data.................................................. 30
Table 10: Propulsion System Comparison. ....................................................................... 41
Table 11: CH4 (SR) – System Load. ................................................................................ 56
Table 12: CH4 (SR) – Fuel Utilization. ............................................................................ 57
Table 13: CH4 (SR) – Turbine Inlet Temperature. ........................................................... 58
Table 14: CH4 (SR) – Gas Turbine Shaft Speed. ............................................................. 59
Table 15: CH4 (SR) – Compressor Mass Flow Rate. ....................................................... 60
Table 16: CH4 (SR) – Solid Oxide Fuel Cell Voltage...................................................... 61
Table 17: CH4 (SR) – Solid Oxide Fuel Cell Power. ....................................................... 62
Table 18: CH4 (SR) – Gas Turbine Power. ...................................................................... 63
Table 19: JP8 (SR) – System Load. .................................................................................. 64
Table 20: JP8 (SR) – Fuel Utilization. .............................................................................. 65
Table 21: JP8 (SR) – Turbine Inlet Temperature. ............................................................. 66
xi
Table 22: JP8 (SR) – Gas Turbine Shaft Speed. ............................................................... 67
Table 23: JP8 (SR) – Compressor Mass Flow Rate. ......................................................... 68
Table 24: JP8 (SR) – Solid Oxide Fuel Cell Voltage. ...................................................... 69
Table 25: JP8 (SR) – Solid Oxide Fuel Cell Power. ......................................................... 70
Table 26: JP8 (SR) – Gas Turbine Power. ........................................................................ 71
Table 27: H2 – System Load. ........................................................................................... 72
Table 28: H2 – Fuel Utilization. ....................................................................................... 73
Table 29: H2 – Turbine Inlet Temperature. ...................................................................... 74
Table 30: H2 – Gas Turbine Shaft Speed. ........................................................................ 75
Table 31: H2 – Compressor Mass Flow Rate. .................................................................. 76
Table 32: H2 – Solid Oxide Fuel Cell Voltage. ................................................................ 77
Table 33: H2 – Solid Oxide Fuel Cell Power. .................................................................. 78
Table 34: H2 – Gas Turbine Power. ................................................................................. 79
Table 35: CH4 (POX) – System Load. ............................................................................. 80
Table 36: CH4 (POX) – Fuel Utilization. ......................................................................... 81
Table 37: CH4 (POX) – Turbine Inlet Temperature. ........................................................ 82
Table 38: CH4 (POX) – Gas Turbine Shaft Speed. .......................................................... 83
Table 39: CH4 (POX) – Compressor Mass Flow Rate. .................................................... 84
Table 40: CH4 (POX) – Solid Oxide Fuel Cell Voltage. ................................................. 85
Table 41: CH4 (POX) – Solid Oxide Fuel Cell Power. .................................................... 86
Table 42: CH4 (POX) – Gas Turbine Power. ................................................................... 87
Table 43: C3H8 (POX) – System Load. ........................................................................... 88
Table 44: C3H8 (POX) – Fuel Utilization. ....................................................................... 89
xii
Table 45: C3H8 (POX) – Turbine Inlet Temperature. ...................................................... 90
Table 46: C3H8 (POX) – Gas Turbine Shaft Speed. ........................................................ 91
Table 47: C3H8 (POX) – Compressor Mass Flow Rate. .................................................. 92
Table 48: C3H8 (POX) – Solid Oxide Fuel Cell Voltage. ............................................... 93
Table 49: C3H8 (POX) – Solid Oxide Fuel Cell Power. .................................................. 94
Table 50: C3H8 (POX) – Gas Turbine Power. ................................................................. 95
Table 51: JP8 (POX) – System Load. ............................................................................... 96
Table 52: JP8 (POX) - Fuel Utilization. ........................................................................... 97
Table 53: JP8 (POX) – Turbine Inlet Temperature. ......................................................... 98
Table 54: JP8 (POX) – Gas Turbine Shaft Speed. ............................................................ 99
Table 55: JP8 (POX) – Compressor Mass Flow Rate..................................................... 100
Table 56: JP8 (POX) – Solid Oxide Fuel Cell Voltage. ................................................. 101
Table 57: JP8 (POX) – Solid Oxide Fuel Cell Power. .................................................... 102
Table 58: JP8 (POX) – Gas Turbine Power. ................................................................... 103
Table 59: CH4 (IR) – Part Load System Efficiency. ...................................................... 104
Table 60: JP8 (SR) – Part Load System Efficency. ........................................................ 104
Table 61: H2 – Part Load System Efficiecy. .................................................................. 105
Table 62: CH4 (POX) – Part Load System Efficiency. .................................................. 105
Table 63: C3H8 (POX) – Part Load System Efficiency. ................................................ 106
Table 64: JP8 (POX) – Part Load System Efficiency. .................................................... 106
xiii
NOMENCLATURE
Fuel cell active area,
Interconnect area specific resistance, Ω-
Chemical activity of diatomic Hydrogen, dimensionless
Chemical activity of water vapor, dimensionless
Chemical activity of diatomic Oxygen, dimensionless
Gas mixture concentration,
Pre-exponential factor for anode exchange current density, A/
Pre-exponential factor for cathode exchange current density, A/
Electrolyte temperature dependence term 1/K
Resistance pre-exponential factor, dimensionless
Gas mixture specific heat, kJ/kmol-K
Anode effective diffusivity,
Cathode effective diffusivity,
Average anode grain size, μm
Average cathode grain size, μm
Binary gas diffusivity,
E Voltage, V
Energy, W
Anode activation energy, J/mole
Cathode activation energy, J/mole
Nernst Cell Potential, V
Cell potential at standard conditions, V
F Faraday’s Constant, 96485 C/mole
Gibbs free energy of formation, kJ/mole
xiv
Enthalpy, kJ
Convective heat transfer coefficient, W/
Enthalpy of formulation at standard reference state, kJ/mol
Sensible enthalpy at standard reference state, kJ/mol
Sensible enthalpy at STP condition, kJ/mol
Current, A
Current density, A/
Anode limiting current density, A/
Cathode limiting current density, A/
Anode electrode exchange current density, A/
Cathode electrode exchange current density, A/
Specific heat ratio, dimensionless
Coefficient of the anode exchange current density, A/m²
Coefficient of the cathode exchange current density, A/m²
SOFC/GT load, percent
Molecular weight, g/mol
Mass flow rate, kg/s
Species flow rate, kmole/s
Number of electrons transferred anode side, dimensionless
Number of electrons transferred cathode side, dimensionless
Power, kW
Power density, W/
Total mixture pressure, atm
Partial pressure of diatomic Hydrogen, atm
Partial pressure of water vapor, atm
Partial pressure of diatomic Oxygen, atm
Standard reference pressure, atm
Pressure ratio, dimensionless
Heat, W
Ratio of anode grain contact neck length to grain size, dimensionless
xv
Ratio of cathode grain contact neck length to grain size, dimensionless
Average anode pore radius, micron
Average cathode pore radius, micron
Universal gas constant, J/mole-K
Reaction rates for each gas species, kmol/s
Temperature, K
Volume,
Work, kW
Gas species mole fraction, kmol
Altitude, ft
Number of electrons transferred for each molecule of fuel
Symmetry coefficient, dimensionless
Electrolyte thickness, μm
Anode electrode porosity, dimensionless
Cathode electrode porosity, dimensionless
Anode activation polarization, V
Cathode activation polarization, V
Compressor design efficiency, dimensionless
Anode concentration polarization, V
Cathode concentration polarization, V
Electrolyte ohmic polarization, V
Interconnect ohmic polarization, V
Turbine design efficiency, dimensionless
Fuel Utilization
Anode electrode tortuosity, dimensionless
σ Leonard-Jones collision diameter, angstrom
Ω Diffusion collision integral, dimensionless
xvi
xvii
ACKNOWLEDGEMENTS
I have learned so much through this journey of pursuing an advanced degree in
mechanical engineering. Through this process, I have enhanced my engineering,
mathematical, and communication skillsets, thus growing as an engineer. I have
encountered many people during this time whom have contributed a great deal to my
education.
I would first like to thank my thesis advisor, Dr. Rory Roberts, for the opportunity
to conduct this research and pursue an advanced degree in engineering. Without all of his
time and financial support contributed, this would not have been possible. Whenever I
would run into an issue with my model and be completely stuck, he would provide
enough guidance to set me off in the right direction. Not only did he provide guidance
with my research, but he also provided guidance with any questions I had about course
selection.
I would also like to thank my committee member Dr. Scott Thomas. His office
door was also open for additional help. If I needed to have someone there to just listen
while I talked through a problem, engineering or personal, he was available. I would like
to thank my other committee member Dr. Hong Huang for taking time out of her busy
schedule to review this thesis and attend my defense presentation.
Last but not least I would like to thank my wonderful family and friends. Without
their unconditional support, this would have been a much harder journey. During the long
nights and stressful times, they were always there for me. I couldn’t have asked for better
support during my studies.
1
INTRODUCTION
As unmanned aerial vehicles (UAVs) become more advanced and continue to
push the envelope, the need for a high efficiency, long endurance propulsion system that
is capable of supporting large onboard electrical loads increases. The integration of a gas
turbine (GT) with a solid oxide fuel cell (SOFC) has already proven to be an efficient and
useful means of stationary power generation. Traditional solid oxide fuel cell hybrid gas
turbine (SOFC/GT) power systems are composed of components that are not ideal for an
airborne platform, such as heavy heat exchangers, motor driven blowers, and separate
combustion regions. The integration of a SOFC combustor hybrid GT system eliminates
the need for such heavy equipment by combining the SOFC and combustor regions,
along with strategic plumbing in which chemical recuperation is achievable. With the
integration of a fuel cell module to a GT engine, these hybrid systems can have lower
power degradation characteristics at high altitude conditions compared to traditional heat
based power systems. Traditional heat based power systems have large performance
degradations at higher altitudes. This power degradation is coupled with the lower
available air supply from the compressor. For example, the Capstone C30 micro turbine
drops to 45 percent of the maximum power at 20,000 feet, which is a 55 percent
degradation in power (Capstone 2006). The majority of the available published research
talks about stationary SOFC/GT system performance and modeling, while select few
discuss applications for airborne platforms. Although this is true, stationary and mobile
SOFC/GT’s share the same unique component, the SOFC. The physics and chemistry
behind the operation of the SOFC remains the same between both applications, therefore
2
much can be learned and applied to airborne platforms by studying stationary systems.
Several publications were reviewed that pertain to this area of research and were used to
provide guidance.
Chinda and Brault (2012) of the College of Industrial Technology at King
Mongkut’s University of Technology, North Bangkok, have created a SOFC/GT power
system numerical model for an auxiliary power unit. Their auxiliary power unit was
designed to deliver 440 kW of net electrical power for a long-range, 300 passenger
aircraft. Their SOFC/GT hybrid model achieved system efficiencies of 45.1 percent,
compared to a similar model with cycle efficiency of 42.0 percent. The high efficiency
system was achieved by conducting an analysis to determine the optimal configuration of
the SOFC, compressor, combustor, heat exchanger, and GT. The configuration that
Chinda’s and Brault’s used was the following: air gets compressed via a compressor, the
air is then heated by exhaust gases from the gas turbine exit via a heat exchanger, then
both air (oxidant) and hydrogen (fuel) is supplied to the SOFC. The SOFC produces
electricity along with high pressure and high temperature exhaust. The unspent SOFC
fuel and high temperature and pressure SOFC cathode exhaust is then combusted in a
combustor. This created heat is then used to preheat the fuel going into the SOFC and is
sent to the turbine to expand and generate even more electrical power. This set up allows
for the SOFC to be self-sustaining in terms of temperature balance across the cell stack.
Utilizing the waste heat from the SOFC in the gas turbine increases the cycle efficiency.
This study showed that with certain flow rates and heat transfer coefficients, extreme
temperatures could be reached, hurting the performance of both the compressor and gas
3
turbine. Using this study, the authors were able to optimize their fuel and oxidant flow
rates to achieve an optimum cycle efficiency of 45.1 percent.
Freeh, Pratt, and Brouwer (2004) developed SOFC and fuel processing models
that were incorporated into the Numerical Propulsion Systems Simulation (NPSS)
software package. The NPSS is a National Aeronautics and Space Administration
(NASA) computing architecture that is used to aid in numerical propulsion system
modeling. A generic SOFC/GT system, not optimized for any parameters, was modeled
within the NPSS software package to evaluate combined model capability. The system
modeled consisted of an SOFC, compressor, turbine, steam reformer, and multiple heat
exchangers. A kerosene type jet fuel Jet-A, modeled as , was used as the main fuel
source for the simulation. The SOFC/GT system hybrid was designed to run at 200 kW of
net electrical power. Of the 200 kW produced, the SOFC made up 186 kW of the total
electrical output. In their model, the SOFC was operated at a cell voltage of E = 0.571
volts, a current density of j = 500 mA/ resulting in a power density of p = 285
mW/ , fuel utilization of μ = 75.0 percent, a stack temperature of 900°C, and a stack
pressure of 4.5 bar. The open circuit and Nernst voltages were reported as = 0.947 V
and = 0.878 V respectively. A compressor adiabatic efficiency of 75 percent and
turbine adiabatic efficiency of 85 percent were used. The turbine inlet temperature was
held to 650°C, while the compressor exit temperature was 243°C. The compressor
pressure ratio used was = 4.94. Having used higher heating value (HHV) for the
incoming fuel energy flow, the thermal efficiency of the modeled system was
approximately 40.6 percent.
4
Chan, S., H. Ho, and Y. Tian (2003) modeled a large scale internal reforming
solid oxide fuel cell and gas turbine power system (IRSOFC-GT) for application in the
residential power supply as a stand alone power station. The system under study
consisted of a combustor, SOFC stack of 40,000 cells, gas turbine, free-rotating power
turbine, two compressors, two recouperators, and a heat-recovery steam generator. This
system was modeled to predict plant performance under full and part load operating
conditions. The fuel cells were operated at a voltage of E = 0.619 volts, a current density
of j = 250.7 mA/ , and a fuel utilization of μ = 85 percent. The net power output of the
plant was = 1700 kW with a net thermal efficiency of 80.5 percent, lower heating value
(LHV). This study showed that plant efficiency was maximum at full load operation. At
part load operation, operating at 56.8 percent of full load, the electrical efficiency
degraded by 22.6 percent. Chan, S., H. Ho, and Y. Tian (2003) concluded that in a large
scale SOFC/GT power plant, it is cost-effective to operate by direct combustion of the
incoming fuel, thus imporving gas turbine performance under part load operation.
Aguiar, P., C.S. Adjiman, and N.P. Brandon (2004) developed a one-dimensional
dynamic anode supported planar solid oxide fuel cell stack model. The model used mass
and energy balances along with electrochemical principles to relate anode and cathode
compositions to SOFC voltage, current density, and power density. The perforamce was
analyazed for co-flow and counter flow operation at several temperatures, T = 1073,
1023, and 973 k (800, 750, and 700 °C ) and for various fuel utilizations, μ = 0, 50, 75,
and 80 percent. The maximum power density for the planar SOFC occurred with a fully
reformed fuel mixture at 1073 k. The fuel was fully reformed internally within the first 20
percent of the length of the cell. The power and current density was p = 0.86 W/ and
5
j = 2.1 A/ , respectfully, with an operating voltage of E = 0.42 V. A secondary fuel
was analyzed, 10 percent pre-reformed methane at μ = 75 percent fuel utilization. With
this fuel mixture, the SOFC operated at E = 0.66 volts and a power density of p = 0.33
W/ at 75 percent fuel utilization.
Kimijima, Komatsu, and Szmyd (2010) numerically modeled a 220 kW solid
oxide fuel cell gas turbine hybrid system at sea-level. Their system was based off of work
previously conducted by Song, Sohn, Kim, Ro, and Suzuki (2005) that created a quasi-
two dimensional model of a tubular SOFC/GT hybrid system. This system consisted of a
compressor, turbine, SOFC module, two recuperators, a desulfurizer and an electric
generator. The exhaust gas from the SOFC was sent to the turbine to generate mechanical
power. The thermal energy from the turbine exhaust was recovered in a recuperator and
used to pre-heat the incoming fuel and air. The incoming fuel is desulfurized prior to
entering the SOFC. Of the 220 kW total power output, the gas turbine contributed 45 kW.
The compressor and turbine efficiencies were 78 and 82 percent respectively. The turbine
inlet temperature was held to 840°C with a pressure ratio of 2.9. Both recuperators
temperature effectiveness were 89 percent. The SOFC module had an active cell area of
A = 94.5 and a current density of j = 3200 A/ . The SOFC module was modeled
as a pre-reformer, internal reformer, and a cell stack. The only fuel analyzed was
methane, which recirculated from the anode exhaust to be the steam supply for the
reformer. A part load analysis was conducted in terms of power output percentage. This
system showed to have a 60 percent (LHV) power generation efficiency at the design-
point conditions.
6
Dicks (1998) and Clark, Dicks, Pointon, Smith, and Swann (1997) conducted
research on catalysts and fuel reforming processes for fuel cells. Direct steam reforming
(SR) and catalytic partial oxidation (POX) are two attractive methods for producing
hydrogen from hydrocarbon fuels such as natural gas. Reforming fuels by catalytic partial
oxidation is typically less efficient compared to steam reformation. The main reason for
this is because in the partial oxidation reaction, a significant portion of the hydrogen fuel
is oxidized to provide heat necessary for the reaction to occur. To achieve direct steam
reformation, a fuel cell anode material that is chemically-stable must be chosen. The
anode of choice is a Nickel-Yttria-Stabilized Zirconia cermet (Ni-YSZ). This cermet,
when fabricated by means of chemical vapour deposition (CVD) methods, have shown to
be stable for 30,000 hours of operation. One of the most problematic issues with the Ni-
YSZ cermet is that at high operating temperatures, the steam reformation kinetics occur
rapidly, causing much of the fuel to be reformed a short distance from the cell entrance.
This can cause a large thermal gradient across the cell if not properly managed, leading to
mechanical failure.
The main purpose of the present research was to analyze the part load
performance of a solid oxide fuel cell combustor hybrid gas turbine propulsion system at
design and off-design operating conditions for application on unmanned aerial vehicles.
A system level numerical model was created within the MATLAB/Simulink environment
that is capable of capturing both the dynamic and steady-state performance of an anode-
supported SOFC combustor integrated with a commercially-available gas turbine engine
used for remote control aircraft. The design point operation of the hybrid system was for
maximum power at sea level. A steady-state part load performance analysis was
7
conducted for various loads ranging from 10 ≤ L ≤ 100 percent and at varying altitudes
ranging from 0 ≤ Y ≤ 20,000 feet. The load was normalized by the maximum power load
occurring at sea level. This analysis was conducted for different fuel mixtures:
humidified hydrogen, propane, methane, and JP-8 jet propellant. Three different fuel
processing methods were modeled also: a catalytic partial oxidation of propane, methane,
and JP-8 jet propellant, direct reformation of methane internal to the fuel cell, and steam
reformation of the jet propellant. For this analysis, lower heating value (LHV) was used
for fuel energy input and efficiency calculations. For the present steady-state analysis, the
system thermal efficiency was plotted against the normalized load for each altitude and
fuel type. A complete data set including fuel utilization, electrical power (SOFC and GT),
compressor mass flow rate, and turbine shaft speed plotted against the normalized load
for each altitude and fuel type is shown in Appendix F.
BACKGROUND
Fuel cells are an energy conversion device that directly converts the chemical
energy stored in a fuel into electricity through electrochemical reactions that take place at
the electrode – electrolyte interface. This direct conversion of energy is what makes fuel
cells more efficient than traditional combustion engines. Fuel cells have many advantages
over traditional combustion engines. Fuel cells have high efficiencies, fast reaction rates,
silent operation, no moving mechanical parts, continuous power production as long as
fuel and oxidant is supplied, and can be thermally self-sustaining (utilization of high
temperature exhaust gases). Some disadvantages to fuel cells are: expensive processing
cost due to exotic materials for high temperature application and material degradation.
8
There are three main components to a fuel cell: anode, cathode, and electrolyte. The
anode is the electrode where the hydrogen reduction reaction takes place. This is where
the hydrogen fuel loses two electrons, producing positively charged hydrogen ions and
two electrons. These two electrons travel to the cathode via an external circuit, where
they are harnessed to do electrical work. The cathode is the electrode where the oxygen
reduction reaction takes place. This is where oxygen from the air supply gains the two
electrons. The electrolyte is a material that is an ionic conductor and electronic insulator,
thus allowing the hydrogen (in the case of hydrogen ion conducting electrolytes) ions to
diffuse through to the cathode side, while blocking electron transfer. The two
electrochemical half-reactions for hydrogen – oxygen fuel cells with hydrogen
conducting electrolytes, such as the PAFC and PEMFC, are shown below (O'Hare, et al.
2009):
→
+
→
Thus, the total reaction for hydrogen – oxygen fuel cells is shown below:
→
Fuel cells are classified by the type of material the electrolyte is made of. There
are five main types of fuel cells: Phosphoric acid fuel cells (PAFC), polymer electrolyte
fuel cells (PEMFC), alkaline fuel cells (AFC), molten carbonate fuel cells (MCFC), and
solid oxide fuel cells (SOFC), each having their own advantages and disadvantages.
Table 1 below shows the different conducting ions and operating temperatures for the
five fuel cells mentioned above.
9
Table 1: Fuel Cell Characteristics
Fuel Cell Conducting Ion Operation Temperature
PAFC 180 – 210 °C
PEMFC RT – 80°C
AFC 60 – 250°C
MCFC 500 – 650°C
SOFC 600 – 1000°C
When dealing with fuel cells, the key to work potential of a fuel cell lies with Gibbs free
energy. In a chemical reaction, only a certain amount of chemical energy can be
converted to do useful work. From thermodynamics, the Gibbs free energy gives the
maximum amount of energy that is available for useful work. In an electrochemical
process, the available work comes from the movement of electrons as current. The
standard potential or open circuit voltage (OCV) for the above total reaction is given by
(Larminie and Dicks 2003):
Fuel cells have three main irreversibility’s, or polarizations, that cause voltage losses.
These are activation polarizations, ohmic polarizations, and concentration polarizations.
Activation polarizations are losses due to electrochemical reaction kinetics that occur at
the electrode – electrolyte interfaces. Ohmic polarizations are losses due to ionic and
electronic charge transport. Concentration polarizations are losses due mass transport, the
supplying and removal of products and reactants. The combination of the OCV and the
polarizations give an actual cell potential under operating conditions.
10
Solid Oxide Fuel Cells
The two most common geometries of SOFC’s are planar and tubular types. The
planar geometry uses a flat sandwich type stack up of the electrodes and electrolyte. To
maintain fuel and oxidant seperation, this geometry requires additional flow structures to
be constructed for the fuel and oxident streams. The tubular geometry provides added
mechanical stability due to the rigid cylindrical geometry compared to a planar SOFC.
This added mechanical stablility makes the tubular SOFC a better selection for
applicaiton in airborne platforms. Tubular SOFC’s with a capped end further increase the
cell’s mechanical stablility while also reducing the probability of leaks due to the reduced
number of connection points. Fuel cells are typically anode or cathode supported. For the
present research, an anode-supported SOFC was modeled. With an anode-supported fuel
cell, the anode material provides the main support for the cell. The electrolyte and
cathode layers are then applied on top of the anode material, creating the electrode –
electrolyte stack up. Figure 1 below shows a schematic and electrode – electrolyte stack
up for an anode supported SOFC.
Figure 1: Anode Supported SOFC Schematic.
The present SOFC model was modeled after an anode-supported fuel cell with
Yttria-Stabilized Zirconia (YSZ) as the electrolyte, a Nickel – Yttria-Stabilized Zirconia
11
(Ni-YSZ) anode, and a Lanthanum Strontium Manganite – Yttria-Stabalized Zirconia
cathode (LSM-YSZ). Both Ni-YSZ and LSM-YSZ are ceramic mixed ionic-electronic
conductors (MIEC’s). These MIEC’s help increase electrochemical reactivity at both
electrode-electrolyte interfaces, thus leading to increased performance. Oxygen ions
transfer through the YSZ electrolyte by a vacancy hopping process. The introduction of
Yttria to a Zirconia lattice creates oxygen vacancies throughout the lattice. These oxygen
vacancies are created to maintain charge neutrality of the electrolyte. (Caputo, Chao and
Huang 2007) and (Kilo, et al. 2003) have performed detailed work in this area and have
shown that the ionic conductivity of the YSZ electrolyte is maximum when the dopant
concentration is 8 to 10 mole percent . Beyond 10 mole percent , the electrolyte
conductivity decreases. For the present study, a YSZ electrolyte with 10 mole percent
was modeled. To promote sufficient transfer of the oxygen ions through the YSZ
electrolyte, the SOFC must be operated at a high temperature (600-1000°C). This
required high operating temperature makes this type of fuel cell ideal for application in a
gas turbine, after the combustion region.
MATHEMATICAL MODEL
A system level mathematical model of the SOFC combustor / GT system was
created within the MATLAB/Simulink environment. Simulink is a software package that
enables users to simulate and analyze dynamic and steady-state systems. The Simulink
modeling environment uses a block and flow type construction, with a full library of
mathematical blocks. The model created consists of both the SOFC/GT and a system
controller. The present model has the capability to operate with various fuel types and
12
fuel processing methods. The model is also capable of simulating operation at full or part
load at altitudes ranging from 0 ≤ Y ≤ 20,000 feet. To make interfacing with the system
user friendly, all the model parameters and variables are stored in one centralized
Microsoft Excel workbook. These parameters are read into the model by a separate script
file. Once these parameters are read in, the model is ready to be run. The model is run by
a simulation file that opens the SOFC/GT model and applies all the model parameters.
Once these are loaded, the simulation file then loops through all the part loads and
altitudes, exporting data specified by the user. These files are discussed in detail in
Appendix A.
Solid Oxide Fuel Cell Model
The mathematical modeling of the solid oxide fuel cell has been broken into
subsystems. There are subsystems for the cell electrochemistry, anode, and cathode.
Each of the anode and cathode subsystems has been treated as a control volume. In the
present model, the conservation of species, moles, and energy has been accounted for in
each of these subsystems. The conservation of momentum was not accounted for due to
the added complexities to the model.
SOFC Electrochemistry
In solid oxide fuel cell electrochemistry there is one main electrochemical
reaction that takes place within the cell:
13
→
This total reaction can be broken up into two half-reactions, one taking place at the
anode-electrolyte interface and the other taking place at the cathode-electrolyte interface.
These two half reactions are as follows:
→
→
At the anode-electrolyte interface, the diatomic hydrogen fuel reacts with the negatively
charged oxygen ions that have diffused through the electrolyte from the cathode side. The
reaction of the diatomic hydrogen and oxygen ion produces water and two electrons. Due
to the high operating temperature of the SOFC, the water produced is in the form of
steam. At the cathode-electrolyte interface, diatomic oxygen reacts with two electrons
(having conducted from anode to cathode via an external circuit) to produce negatively
charged oxygen ions. These oxygen ions then diffuse through the ionic conducting YSZ
electrolyte. The work done by a fuel cell is in the form of an electric current.
A fuel cell’s electrochemical cell voltage is a function of chemical activity,
species concentration, gas pressure, and temperature. The Nernst potential (Nernst
equation) is the backbone of fuel cell thermodynamics. This equation relates temperature,
gas pressure, and species concentration to the electrochemical cell voltage or open circuit
voltage (OCV) and for the above reaction is given by (O'Hare, et al. 2009):
ln(
⁄
+
14
For an ideal gas assumption, the chemical activity for diatomic hydrogen, diatomic
oxygen, and the water vapor is given by (Koehler, Jarrell and Bond 2001):
This assumption reduces the above Nernst potential equation to the following given by
(Yang, et al. 2013):
ln(
⁄
+
To expand the capability of the model and allow for fuel flexibility, a seven
species reaction vector is utilized. This reaction vector accounts for the consumption and
production of each species:
The reaction rates are related to the current demand of the fuel cell by Faraday’s Law:
Faraday’s law states that the amount of substance consumed or produced at the electrode
interface is directly proportional to the amount of electricity that passes through the cell.
Thus, the more current drawn from the cell, the more reactants consumed and products
produced. Using this relationship and the electrochemical half-reactions for the SOFC,
reaction vectors can be written for both the anode and cathode:
15
SOFC Polarization Losses
Under real operating conditions, a fuel cell operates at a voltage less than that
described by the Nernst equation. This is due to polarizations that inhibit the fuel cell
reaction kinetics, electrical and ionic charge transport, and the convective and diffusive
mass transport. As the current demand from the fuel cell increases, the operational
voltage of the cell decreases due to these polarizations. The operational fuel cell voltage
is calculated by subtracting each of the polarizations from the Nernst potential:
Activation Polarization
In electrochemistry, cell potential is used to drive the electrochemical reactions
and their finite rates. Fuel cell reaction kinetics discusses how the mechanisms behind the
electrochemical reactions behave. In order to convert incoming reactants into products
and produce a voltage, a thermodynamically favorable forward reaction must occur. An
energy barrier must be overcome to produce a forward reaction. The reaction rate, or rate
at which reactants are converted into products, is determined by the probability of a
reactant species overcoming the energy barrier (activation energy). This activation barrier
16
can be reduced by sacrificing some of the available cell potential. This activation
polarization can be solved for by using a modified version of the Butler-Volmer equation:
(
* +
(
*
In this equation, the operational current density is defined as:
There are many different published equations for anode and cathode exchange current
density, relating activation energy and detailed material properties of each electrode. The
anode and cathode exchange current density is calculated as follows:
(
*
(
*
The coefficient of the anode and cathode exchange current density takes into
account electrode specific properties such as porosity and grain size and is given by:
(
√
) [
( ) ]
(
√
) [
( ) ]
The model input parameters for the activation polarization sub-system are shown below
in Table 2.
17
Table 2: SOFC Activation Polarization Model Input Parameters
Input Parameter Anode Cathode
Activation energy, (j/mol) 1.20E+05 1.50E+05
Number of electrons transferred, 2 4
Pre-exponential factor, (A/ 6.479E+03 2.265E+06
Porosity, (dimensionless) 0.40 0.40
Tortuosity, (dimensionless) 2.8 N/A
Average pore radius, (μm) 3 3
Average grain size, 1.5 1.5
Ratio of grain contact neck length to grain size 0.7 0.7
Ohmic Polarization
The ohmic losses in a fuel cell consist of resistance of the ion flow through the
electrolyte and resistance of electron flow through the electrodes. Accumulation and
depletion of electrons on both of the electrodes creates a voltage gradient. This voltage
gradient is what drives the transfer of electrons from electrode to electrode. The same
phenomena occur with the oxygen ions within the electrolyte. The voltage deficit is the
voltage required to overcome the resistances with both the electrodes and electrolyte. The
relationship for this voltage can be determined by using a form of Ohm’s law:
(°C)
The above equation is the voltage loss for the cell interconnects. When multiple cells are
connected together, whether in series or parallel, interconnects are made between each
cell to maintain a complete electrical circuit, thus allowing current to flow from one
current collector to the next. The electronic and ionic ohmic losses are given by (Antloga,
et al. 2005):
18
The total ohmic losses within a fuel cell then become:
The model input parameters for the ohmic polarization sub-systems are shown below in
Table 3
Table 3: SOFC Ohmic Polarization Model Input Parameters
Input Parameter Value
Interconnect area-specific resistance, (Ω/ 0.05
Electrolyte temperature dependence term, (1/K) -3708.5
Resistance pre-exponential factor, 1.6549
Electrolyte Thickness, ( μm)
20
Concentration Polarization
Concentration polarization deals with the losses due to mass transport
phenomena. The two main types of mass transport within a fuel cell are due to diffusive
transport in the electrodes and convective transport in the fuel / oxidant flow channels.
The convective forces within the flow channels are due to the pressure gradients caused
by the pumps and compressors needed to supply fuel and oxidant to the cell. The
diffusive forces within the electrodes are due to species consumption and depletion at the
electrode-electrolyte interface. This results in a concentration gradient, thus driving the
chemical species through the electrodes. The governing equation for the concentration
polarization is given by (O'Hare, et al. 2009):
(
) (
* +
(
) (
*
This equation accounts for both the anode and cathode concentration terms. When
reactant concentrations at the electrode-electrolyte interface drop to zero, this presents a
19
limiting case for the mass transport phenomena. Therefore, the fuel cell cannot handle a
current higher than that of the limiting current density, shown below:
The effective diffusivities for the anode and cathode reaction sites are calculated using
thermophysics principles, Leonard-jones potentials to describe the interaction between
gas species. A detailed explanation of this calculation is discussed in Appendix B. Due
to the porous nature of the fuel cell materials, during diffusion, gas molecules are
restricted. There are many published equations for this diffusion correction, but for high
temperature operation a more accurate model has been determined (Cussler 1995):
The model input parameters for the concentration polarization subsystem are shown
below in Table 4.
Table 4: SOFC Concentration Polarization Model Input Parameters.
Input Parameter Anode Cathode
Symmetry coefficient, 0.5 0.5
Gas mixture concentration, 10,000 10,000
Pre-exponential factor, (A/ 6.479E+03 2.265E+06
Porosity, (dimensionless) 0.40 0.40
Tortuosity, (dimensionless) 2.8 N/A
20
Energy Analysis
A mass and energy analysis has been employed on each of the control volume
subsystems. Momentum conservation was not taken into account for this research due to
the complexities added. The conservation of mass was employed to account for each of
the gas species within the cell:
One assumption made for the mass conservation was that the chemical reactions for each
species occur in a quasi-static nature. Similar to the seven species reaction vector, a seven
species mole fraction vector was created to allow for mass conservation of multiple gas
species:
Mathematically, the total species conservation within the fuel cell becomes:
The conservation of energy was employed to account for all the energy entering
and exiting both the anode and cathode gas streams:
From fundamental thermodynamic energy laws, for a control volume, the energy
equation becomes:
Accounting for the enthalpy flows for both gas streams, the energy equation takes on
another form:
21
[ ]
The gas species specific heat was calculated using a third-order polynomial curve fit
given by (Cengal and Boles 2011):
( )
The specific heat coefficients for different gases are shown below in Table 5.
Table 5: Specific Heat Coefficients for Various Gases.
Gas Formula
Methane 19.89
18
5.024 1.269 -11.01
Carbon Monoxide 18.16
0.1675 0.5372 -2.222
Carbon Dioxide 22.26 5.981 -3.501 -7.469
Hydrogen 29.11 -0.1916 0.4003 -0.8704
Water Vapor 32.24 0.1923 1.055 -3.595
Nitrogen 28.9 -0.1571 0.8081 -2.873
Oxygen 25.48 1.52 -0.7155 1.312
The enthalpy of the gas streams were calculated by integrating the third-order polynomial
equation for the specific heat of each gas, with respect to temperature:
∫ ( )
The heat transfer accounted for in the present model consists for the convective heat
transfer of the gas streams, the heat generated due to ohmic heating, and heat form the
water gas shift. Heat due to radiative heating was not taken into account for in this model
because a single cell was analyzed. To simulate a SOFC stack, the incoming and
outgoing flow rates of the fuel and oxidant were manipulated to simulate a user-specified
stack size. The heat produced due to ohmic heating was calculated as follows:
22
Combustor Model
The combustor modeled is used to combust the unspent fuel from the anode-off
gas stream. The combustion chamber was treated as a single gas phase reactor and
assumed achieve complete combustion adiabatically. For the combustion subsystem, a
conservation of mass and energy was employed, very similar to that in the above sections
of this paper. The governing energy conservation equation used for this process, as
defined by fundamental thermodynamic principles is given by:
The combustor was modeled as a dynamic energy conversion equation. Assuming a
steady-state combustion process, the heat output was calculated by:
∑ ∑
The assumption of adiabatic combustion forces the enthalpy flow of the reactants to equal
the enthalpy flow of the products:
∑ ∑
This is an iterative process, upon which the adiabatic flame temperature can be
calculated.
Gas Turbine Model
The gas turbine modeled for these simulations are based off parameters from a
single-shaft, commercially-available remote control aircraft jet engine, the Jet Cat P-80
manufactured by Jet Cat USA. This engine is capable of producing 22 pounds of thrust at
a maximum shaft speed of 125,000 revolutions per minute (USA 2014). The gas turbine
model consists of a low pressure compressor, low pressure shaft, and low pressure
23
turbine. The model loads in engine maps containing normalized parameters such as
pressure and shaft speed. The compressor and turbine outlet temperatures were calculated
using isentropic compression and expansion relationships given by (Cengal and Boles
2011):
(
(
(
)*+
( (
(
)
),
The specific heat ratio for an ideal gas was given by (Cengal and Boles 2011):
The compressor and turbine work was calculated from the enthalpy differential between
the inlet and exit states:
( )
( )
The low pressure shaft was modeled to calculate rotational speed by accounting for the
compressor load, turbine load, and engine input load. The shaft model assumes operation
is such that there is no friction. Table 6 below lists compressor and turbine properties
used in this study.
24
Table 6: Gas Turbine Model Input Parameters.
Input Parameter Value
Design pressure ratio, 3.7
Design mass flow rate, (kg/s) 0.09
Design speed, (rev/min) 125,000
Compressor efficiency, 0.7
Turbine efficiency, 0.7
SOFC Combustor / GT Model
The unique integration of the SOFC combustor and the GT engine is really what
makes this system different from other published SOFC/GT hybrids. A traditional gas
turbine engine schematic is shown below in Figure 2.
Figure 2: Traditional Gas Turbine Engine Schematic.
In this system fuel and high pressure oxidant are combusted in a combustion chamber to
produce high temperature exhaust gas. This high temperature exhaust gas is then sent to
expand within the turbine, thus creating thrust or turning and electrical generator. The
problem with this system is the inefficient conversion of chemical energy within the fuel
to useful energy. For UAV systems, this useful energy is typically in the form of
electrical work or mechanical (propulsive) work. The traditional system wastes energy
25
during the conversion process from chemical energy to thermal / heat energy. Each
energy conversion process involves a degradation of the quality of the energy, starting
out as high quality chemical energy and ending up as lower quality thermal energy.
The SOFC combustor / GT modeled takes advantage of the wasted energy
described above. A fuel cell stack can be integrated into the system to produce additional
electrical energy at a very low expense, while still maintaining a high quality exhaust gas
stream to be sent to the turbine engine. The only drawback to the system is the added
weight of the fuel cell stack. The SOFC/GT system modeled is shown below in Figure 3.
Figure 3: SOFC/GT Schematic.
In this hybrid system, the compressor and turbine operate like they would in a
traditional system but in addition; air and fuel are sent to the SOFC, producing additional
electricity capable of powering onboard electronics or sustaining other electrical loads
needed during flight. The unique feature about this system is the plumbing of the SOFC
combustor to the GT engine. Figure 3 shows all major components and plumbing
between the GT and SOFC combustor. The system has been broken into seven different
states to give an in depth look at operational characteristics. States 1 – 2 represents the
26
compression of atmospheric air. The fuel is supplied at state 6 at the anode inlet. The
compressed air and unspent fuel from states 2 and 7 mixes together and combusts in the
combustion chamber, resulting in non-oxygen depleted high temperature combustion
products. The high temperature combustion products are then sent to the cathode side of
the SOFC. The cathode stream temperature increases as it travels down the cell due to
heat generation within the cell. The high temperature exhaust is then expanded in the
turbine between states 4 and 5. Power is produced between states 6 and 7 from a direct
conversion of fuel energy to electrical energy through electrochemical reactions and
between States 4 and 5 from the expansion of hot SOFC exhaust through the GT. This
configuration has many benefits such as the utilization of waste heat of the cathode-off
steam and pressurized stack operation. The pressurized operation of the fuel cell stack
helps increase performance by allowing the electrochemical reaction kinetics to occur at a
faster rate.
RESULTS AND DISCUSSION
To ensure that the SOFC model was operating close to reality, a series of
experiments were conducted on a tubular SOFC. There experiments consisted of voltage-
current density tests for various temperatures and fuel utilizations. The SOFC model
performance correlated well with the experimental data from the voltage-current density
tests. This data is now shown here due to limitations necessary for protecting intellectual
property.
27
Steady-State Part Load Performance Analysis
The SOFC/GT model was sized for maximum power operation at sea-level and
for this research, the SOFC stack was sized to the commercially-available gas turbine
parameters. A mathematical controller was modeled to maintain a turbine inlet
temperature of 1093 k and a fuel cell stack temperature gradient of 170°C, which was set
to maintain chemical stability within the cell. During scoping runs, the fuel utilization of
the SOFC cell was not allowed to change; this caused the cell temperature gradient to
exponentially increase at lower part loads. It was then determined that the fuel utilization
needed to be flexible to maintain the 170°C gradient through all operating conditions.
A steady-state part load performance analysis was conducted using the SOFC
Combustor / Hybrid GT model over an altitude range of 0 ≤ Y ≤ 20,000 feet and a part
load range of 10 ≤ L ≤ 100 percent. This analysis was conducted for four different fuel
types: humidified hydrogen, methane, propane, and JP-8 jet fuel. The humidified
hydrogen model operated on a fuel composition of 97 percent hydrogen 3 percent water
vapor. Methane fuel was modeled two ways: a catalytic partial oxidation (POX) of the
methane gas and direct reformation of the methane internal to the cell through steam
reformation (SR). The propane case was modeled using a catalytic partial oxidation of the
propane gas. The JP-8 (Jet Propellant 8) was modeled two ways: a catalytic partial
oxidation of the JP-8 in an air POX reactor and steam reformation using added heat from
the SOFC. In both fuel processing methods, the JP-8 was fully reformed, no
hydrocarbons present in the reformation products. The hydrogen yield for each of the fuel
28
processing methods modeled is shown below in Table 7. A detailed chemical analysis of
the fuel processing methods is discussed in Appendix C.
Table 7: Fuel Processing - Hydrogen Yield.
Fuel Hydrogen Yield (
– Steam Reformation 80 %
– Partial Oxidation 75 %
JP-8 – Steam Reformation 75 %
JP-8 – Partial Oxidation 67.5 %
– Partial Oxidation 70 %
As mentioned above, each model was sized to operate at maximum power at sea-
level. Maximum power was determined by increasing the system load until the voltage
reached the minimum operating point of = 0.5 volts (user-defined) and both the turbine
inlet temperature and SOFC temperature gradient criteria were met. Once this occurred,
the maximum load and total system power was established. The total system power is the
sum of the SOFC and GT power outputs. If the criteria were not met, the load and fuel
cell stack size was varied and the process was repeated. The system power results for
each model are summarized below in
Table 8.
Table 8: Maximum System Sizes – Sea-Level at Full Load
Fuel Number
of Cells
SOFC Power
(kW)
GT Power
(KW)
Total Power
(kW)
– Steam Reformation 215 22.85 5.12 27.97
JP-8 – Steam Reformation 200 21.49 5.21 26.7
- Humidified 180 21.34 4.63 25.97
– Partial Oxidation 180 19.76 5.08 24.84
JP-8 – Partial Oxidation 180 19.39 5.45 24.84
– Partial Oxidation 180 19.49 5.25 24.74
29
The part load performance analysis showed that the model with the highest
system efficiency, and highest sea-level efficiency, was the SOFC/GT systems operating
on the direct internal steam reformation of methane and JP-8. This can be explained by
the systems thermal heat sink capacity. The heat sink capacity of the systems modeled
were limited by the gas turbine, thus the fuel cell stacks were sized to fit the fixed thermal
sink capacity. The systems utilizing steam reformation of the fuel increases the overall
system thermal heat sink capacity due to the endothermic nature of the steam reformation
reaction. The methane and JP-8 steam reformation systems produced the highest
efficiencies because during the steam reformation, heat is absorbed within the fuel cell
due to the steam reformation reaction. The absorption of this heat reduces the overall
temperature of the SOFC, thus dropping the turbine inlet temperature from the 1093 k set
point. This allows the fuel cell stack size to be increased. The larger stack size
subsequently results in a larger net power output from the SOFC. The internal steam
reformation of the methane not only increases power output from the cell, it also helps
with the cell thermal management and chemical recuperation through reforming with
waste heat. The part load performance efficiency data from the model is summarized
below in Table 9.
30
Table 9: Part Load Performance Efficiency Model Data.
The SOFC/GT system running on steam reformation of methane has a system efficiency
that is 3 percent higher than that of the steam reformed JP-8, 30.4 percent higher than that
of the humidified hydrogen system, 40.9 percent higher than that of the partial oxidation
of methane system, 56 percent higher than that of partial oxidation of JP-8 system, and
51.9 percent higher than that of the partial oxidation of propane system. System
efficiency versus part load for each fuel type has been plotted in Figure 4 through Figure
6.
Fuel
Total
Power
(kW)
Max.
Efficiency
(%)
Sea-Level
Efficiency
(%)
– Steam Reformation 27.97 46.8 33.85
JP-8 – Steam Reformation 26.7 45.4 33.13
- Humidified 25.97 35.88 26.46
– Partial Oxidation 24.84 33.2 24.71
JP-8 – Partial Oxidation 24.84 30.0 22.39
– Partial Oxidation 24.74
30.8 22.93
31
(a)
(b)
Figure 4: System Efficiency versus Part Load: (a) Sea-Level; (b) 4,000 ft.
32
(a)
(b)
Figure 5: System Efficiency versus Part Load: (a) 8,000 ft; (b) 12,000 ft.
33
(a)
(b)
Figure 6: System Efficiency versus Part Load: (a) 16,000 ft; (b) 20,000 ft.
34
Figure 4 through Figure 6 clearly show how much of an impact on system
efficiency utilizing the natural internal reformation of methane fuel has. This internal
reformation is capable of being conducted because of the high operating temperature of
the SOFC, therefore no exotic internal catalyst would be needed to perform the fuel
reformation, unlike in an air POX reactor. In each of the cases, the maximum efficiency
occurs around 40 to 50 percent load. System efficiency drops off below 40 percent and
above 50 percent load. Operating below 40 percent load, the SOFC/GT system efficiency
significantly decreases. This is because below 40 percent load, the turbine speed saturates
at its minimum speed of 55,000 revolutions per minute. This results in the systems
inability to decrease the air mass flow rate through the system via the GT, consequently
causing the SOFC temperature gradient to rise above the 170°C set gradient. In order to
maintain this temperature gradient, the fuel utilization of the fuel cell must drop, sending
more fuel to the combustor. This increases the cathode inlet stream temperature, thus re-
establishing the SOFC temperature gradient. This causes a drop in system efficiency
because the system is no longer using fuel to produce additional electricity from the fuel
cell, but rather just for combustion purposes to maintain temperature. At loads below 40
percent, the hybrid SOFC/GT system starts acting like a traditional GT system and all the
added benefits of the hybrid system go to waste. System efficiency is lower at loads
higher than 50 percent design load. At these loads, the system fuel utilization is constant
but due to the increasing load the GT is continuously speeding up, bringing in more
cooling flow until it is saturated at its upper limit of 125k RPM at 100 percent design
load. The increased load causes the SOFC to drop in voltage, resulting in a less efficient
state of operation. To maintain constant fuel utilization, the fuel flow rate is increased.
35
This increases the fuel energy introduced to the system. The power produced by the
SOFC and GT due to this increased load is not significant compared to the additional fuel
energy brought into the system, thus resulting in lower calculated system efficiencies. To
show these relationships, the fuel utilization, compressor mass flow rates, and SOFC
voltage for the internally reformed methane is plotted versus part load in Figure 7 through
Figure 9 below.
Figure 7: Fuel Utilization versus Part Load – CH4 (SR).
36
Figure 8: Compressor Mass Flow versus Part Load – CH4 (SR).
Figure 9: Solid Oxide Fuel Cell Voltage versus Part Load – CH4 (SR).
These trends were consistent for each fuel type. The system efficiency versus part
load operation for each of the individual fuel types has been plotted in Figure 10 through
Figure 15, from sea-level to a ceiling of 20,000 feet. As altitude increases, the maximum
37
load available at each altitude decreases. This is due to a decrease in air density and thus
a lower mass flow rate for the same turbine speed. Due to the decrease in the amount of
cooling air coming into the system, the load must be decreased to maintain the cell
temperature gradient. For each system, the maximum load available decreases from 100
percent at sea-level, to approximately 78-80 percent at 20,000 feet.
Figure 10: System Efficiency versus Part Load: Methane Steam Reformation.
38
Figure 11: System Efficiency versus Part Load: JP-8 Steam Reformation.
Figure 12: System Efficiency versus Part Load: Humidified Hydrogen.
39
Figure 13: System Efficiency versus Part Load: Methane Partial Oxidation.
Figure 14: System Efficiency versus Part Load: Propane Partial Oxidation.
40
Figure 15: System Efficiency versus Part Load: JP-8 Partial Oxidation.
Impact to UAV Performance
A numerical comparison between a current UAV with a traditional heat based
propulsion system and the system analyzed in this study was conducted. The Predator’s
Rotax 914 four cylinder turbo-prop was compared against the fuel cell combustor hybrid
gas turbine system operating on steam reformed JP-8. Parameters that were compared
were engine weight, engine power density, fuel capacity, system power, and potential
work. This comparison is shown below in Table 10. The fuel cell combustor hybrid gas
turbine system is a heavier system, approximately 122.7 kg compared to the Rotax 914 at
78 kg. However, the SOFC/GT system has a much higher average system efficiency of
46 percent compared to 20 percent from the Rotax 914. Using the same fuel energy and
system wet weights; the SOFC/GT system analyzed in this research has more than
doubled the potential work compared to the Predator’s Rotax 914 propulsion system. A
UAV using this fuel cell combustor gas turbine hybrid propulsion system could achieve
41
much longer loiter durations during a mission compared to current UAV traditional heat
based propulsion systems.
Table 10: Propulsion System Comparison.
Propulsion System Comparison
Specifications Rotax 914 SOFC/GT
Fuel Energy [kW-hr/kg] 11.97 11.97
System Weight dry [kg] 512.0 556.7
System Weight wet [kg] 1,020.0 1,020.0
Engine Volume [L] 185.2 237.0
Engine Weight [kg] 78.0 122.7
Engine Power Density [kW/kg] 0.94 0.44
Engine Power Density [kW/L] 0.39 0.23
Fuel Capacity [kg] 508.0 463.3
System Power [kW] 73.0 54.0
Average System Efficiency 20% 46%
Potential Work [kW-hr] 1,216.4 2,551.3
42
CONCLUSIONS
A solid oxide fuel cell combustor gas turbine hybrid power system model for
application in unmanned aerial vehicles was developed within the MATLAB/Simulink
mathematical modeling software package. A steady-state part load performance analysis
was conducted using the SOFC Combustor / Hybrid GT model over an altitude range of 0
≤ Y ≤ 20,000 feet and a part load range of 10 ≤ L ≤ 100 percent. This analysis was
conducted for four different fuel types: humidified hydrogen, methane, propane, and JP-8
jet fuel. The humidified hydrogen model operated on a fuel composition of 97 percent
hydrogen 3 percent water vapor. Methane fuel was modeled two ways: a catalytic partial
oxidation of the methane gas (POX) and direct reformation of the methane internal to the
cell through steam reformation (SR). The propane case was modeled using a catalytic
partial oxidation of the propane gas. The JP-8 (Jet Propellant 8) was modeled two ways: a
catalytic partial oxidation of the JP-8 in an air CPOX reactor and steam reformation using
added heat from the SOFC. A system controller was modeled to maintain a turbine inlet
temperature of 1093 k and keep the solid oxide fuel cell temperature gradient at 170°C,
thus maintaining chemical stability within the cell.
It was found that if the fuel utilization of the fuel cell was not allowed to vary
with load and altitude, at part loads approximately lower than 40 percent, the fuel cell
temperature gradient exponentially increased. This was caused by a dramatic decrease in
cooling air due to the gas turbine being at its minimum shaft speed. The fuel cell
temperature gradient was successfully maintained once the fuel utilization was flexible.
Each system was sized to operate at maximum power at sea-level. As altitude increased,
it was observed that the maximum load decreased. This is due to the decrease in air
43
density and thus a lower mass flow rate for the same turbine speed. The maximum load
dropped from 100 percent at sea-level to approximately only 80 percent, of the maximum
sea-level load, at 20,000 feet, which is 20 percent degradation in power. Traditional heat
based power systems have larger power degradations at part load operation, such as the
Capstone C30 micro turbine having a 55 percent power degradation at 20,000 feet. The
maximum system efficiency for each fuel type occurred around part loads of 40 ≤ L ≤ 60
percent. The most efficient system was found to be the SOFC/GT model that operated on
internally steam reformed methane. This reformation process is only able to happen
naturally due to the high operating temperature of the SOFC (˃ 600°C). This reformation
process is so advantageous to an airborne system because it allows for a larger fuel cell
stack for the same gas turbine size. This increase in stack size not only increases the net
power produced by the system, but also the overall system efficiency. The steam
reformed methane showed to have an efficiency at sea level of 33.85 percent and a
maximum efficiency at an altitude to L = 20,000 feet of 46.8 percent, with a stack size of
215 cells and a net power output of 27.87 kW. The increased performance at part loads at
altitude is opposite that of a traditional gas turbine engine. The hybrid system modeled
does not show the same performance degradation as current UAV systems have at part
loads, operating on traditional Brayton and Otto cycles.
A comparison between current UAV propulsion technology, such as the Rotax
914, and the fuel cell combustor system in this study showed that the hybrid system has
approximately double the work potential than the Rotax 914 (SOFC/GT with 2,551 kW-
hr, Rotax 914 with 1,216 kW-hr). The present analysis shows that the part load
performance of a SOFC/GT hybrid system depends heavily on the characteristics of the
44
fuel cell combustor. The thermal management of these hybrid systems is crucial to
system performance, both full load and part load. Failing to manage the thermodynamics
of these systems will lead to a cascading effect ultimately resulting in system failure.
Since the majority of a UAV’s mission is during loiter, being able to operate at a higher
efficiency at part load seen during loiter will significantly increase mission duration and
mission range. This model can be further expanded upon to perform a dynamic analysis
on other aspects of the solid oxide fuel cell combustor gas turbine hybrid operating cycle.
By continuing this work and building upon mathematical models like the present, it will
allow us to continue learning about the integration, operation, and management of these
hybrid systems.
45
APPENDIX A: MATLAB/SIMULINK MODEL FILES
To make this mathematical model user-friendly, the number of files needed to run
simulations was minimized. All model parameters are stored in one Microsoft Excel file.
Each component to the model has its own Excel sheet full of parameters. A MATLAB
scrip file was written to read in every parameter from the Excel file using MATLAB’s
“xlsread” command. In doing this, if a user needed to make a parameter change and re-
run a simulation, all they would need to do would be update the Excel workbook and
save. This file organization relieves a lot of complexities that can be involved in
computer aided numerical modeling. To run the model, another script file was written. It
is in this file where the user is able to specify what data is to be saved from the
simulation. This file allows the simulation to be run without having to have the model file
physically open. All files needed for the simulation must be in the same folder. The
sequence to running a simulation is as follows:
1.) Apply parameters to the model:
a. Run “SOFC_GT_OpenModel” file
2.) Specify which model to run and what simulation data to record and execute:
a. Run “Run_Simulaiton” file.
To help with debugging purposes, multiple progress bars were added to show the user
exactly what part load and altitude the model was currently running. This is helpful when
there are issues with the model; the user knows exactly what case was being simulated,
thus cutting down on debugging time. These files are shown below.
46
47
48
49
50
51
APPENDIX B: EFFECTIVE DIFFUSIVITY: LEONARD-JONES POTENTIALS
The effective diffusivity has been calculated using the Chapman-Enskog Theory
which has been proven to be accurate to approximately eight percent. In kinetic gas
theory, diffusivity is dependent on both the properties of the particle doing the diffusing
and the particles that are being diffused. Typically i denotes the diffusing party and j
denotes the party being diffused. To calculate the binary gas diffusion coefficient, a
weighted average of all seven gas species has been taken. The interaction between the
particles has been accounted for using Leonard-Jones potential parameters such as
collision diameter and collision integrals.
Binary Diffusion Coefficient:
[ (
*
]
Leonard-Jones Collision Diameter:
Leonard-Jones Potential Parameters found from Viscosities (Klein, et al. 1974)
Substance σ( ) ε/k (K)
Methane 3.758 148.6
Carbon Monoxide 3.69 91.7
Carbon Dioxide 3.941 195.2
Hydrogen 2.827 59.7
Water 2.641 809.1
Nitrogen 3.798 71.4
Oxygen 3.467 106.7
52
Collision Integral Tabulated Data from (Klein, et al. 1974)
kT/e Ω kT/e Ω kT/e Ω kT/e Ω
0 10 1.3 1.273 2.7 0.977 4.8 0.8492
0.3 2.662 1.35 1.253 2.8 0.9672 4.9 0.8456
0.35 2.476 1.4 1.233 2.9 0.9576 5 0.8422
0.4 2.318 1.45 1.215 3 0.949 6 0.8124
0.45 2.184 1.5 1.198 3.1 0.9406 7 0.7896
0.5 2.066 1.55 1.182 3.2 0.9328 8 0.7712
0.55 1.966 1.6 1.167 3.3 0.9256 9 0.7556
0.6 1.877 1.65 1.153 3.4 0.9186 10 0.7424
0.65 1.798 1.7 1.14 3.5 0.912 20 0.664
0.7 1.729 1.75 1.128 3.6 0.9058 30 0.6232
0.75 1.667 1.8 1.116 3.7 0.8998 40 0.596
0.8 1.612 1.85 1.105 3.8 0.8942 50 0.5756
0.85 1.562 1.9 1.094 3.9 0.8888 60 0.5596
0.9 1.517 1.95 1.084 4 0.8836 70 0.5464
0.95 1.476 2 1.075 4.1 0.8788 80 0.5253
1 1.439 2.1 1.057 4.2 0.874 90 0.5256
1.05 1.406 2.2 1.041 4.3 0.8694 100 0.513
1.1 1.375 2.3 1.026 4.4 0.8652 200 0.4644
1.15 1.346 2.4 1.012 4.5 0.861 400 0.436
1.2 1.32 2.5 0.9996 4.6 0.8568 - -
1.25 1.296 2.6 0.9878 4.7 0.853 - -
53
APPENDIX C: SOFC/GT FUEL CHEMISTRY
Besides the humidified hydrogen case, the two main fuel processing methods
modeled in the present model were with steam reformation and catalytic partial oxidation
of the fuels. In a steam reformation reaction, a hydrocarbon fuel reacts with steam at high
temperatures to produce carbon-monoxide, carbon-dioxide, hydrogen, and water in the
vapor state. Steam reformation is an endothermic reaction (absorbs energy). Steam
reformation typically has the highest hydrogen yield because steam reforming does not
react any oxygen, therefore does not cause a dilution of the air by nitrogen. To further
increase the hydrogen yield of this process, the carbon-monoxide can be shifted to
hydrogen in a water-gas shift reaction. In this reaction, carbon-monoxide reacts with
water vapor to produce carbon-dioxide and hydrogen. Partial oxidation reforming reacts a
hydrocarbon fuel with oxygen in the air to partially combust (oxidize) the fuel. This
reformation process is usually done with a catalyst. The chemical formulas used for these
reactions are given by (O'Hare, et al. 2009):
Hydrogen Yield:
Steam Reformation:
↔ (
*
Catalytic Partial Oxidation:
↔
54
Water-Gas Shift:
↔
55
APPENDIX F: SUMMARY OF SOFC/GT MODEL DATA
The following pages present the steady-state data recorded from the SOFC/GT
model part-load simulations for each fuel type and altitude.
56
Table 11: CH4 (SR) – System Load.
Part Load (A) – CH4 (IR)
Load
(%)
Altitude (ft) 0E+0 2E+3 4E+3 6E+3 8E+3 10E+3 12E+3 14E+3 16E+3 18E+3 20E+3
10 21.0 19.9 19.0 18.2 17.3 16.5 15.7 15.0 14.2 13.4 12.7 20 42.0 39.8 38.0 36.4 34.6 33.0 31.4 30.0 28.4 26.8 25.4 30 63.0 59.7 57.0 54.6 51.9 49.5 47.1 45.0 42.6 40.2 38.1 40 84.0 79.6 76.0 72.8 69.2 66.0 62.8 60.0 56.8 53.6 50.8 50 105.0 99.5 95.0 91.0 86.5 82.5 78.5 75.0 71.0 67.0 63.5 60 126.0 119.4 114.0 109.2 103.8 99.0 94.2 90.0 85.2 80.4 76.2 70 147.0 139.3 133.0 127.4 121.1 115.5 109.9 105.0 99.4 93.8 88.9 80 168.0 159.2 152.0 145.6 138.4 132.0 125.6 120.0 113.6 107.2 101.6 90 189.0 179.1 171.0 163.8 155.7 148.5 141.3 135.0 127.8 120.6 114.3
100 210.0 199.0 190.0 182.0 173.0 165.0 157.0 150.0 142.0 134.0 127.0
Figure 16: CH4 (SR) – System Load versus Part Load.
57
Table 12: CH4 (SR) – Fuel Utilization.
Fuel Utilization ( – CH4 (IR)
Load
(%)
Altitude (ft) 0E+0 2E+3 4E+3 6E+3 8E+3 10E+3 12E+3 14E+3 16E+3 18E+3 20E+3
10 0.216 0.215 0.216 0.217 0.218 0.219 0.220 0.221 0.221 0.221 0.223 20 0.357 0.355 0.357 0.358 0.360 0.361 0.362 0.365 0.365 0.365 0.366 30 0.456 0.454 0.456 0.458 0.459 0.461 0.462 0.465 0.465 0.461 0.450 40 0.529 0.528 0.530 0.531 0.533 0.534 0.527 0.521 0.514 0.505 0.496 50 0.567 0.565 0.563 0.560 0.557 0.553 0.549 0.544 0.538 0.533 0.525 60 0.570 0.569 0.569 0.567 0.565 0.563 0.559 0.557 0.554 0.549 0.544 70 0.571 0.571 0.571 0.570 0.569 0.567 0.566 0.564 0.562 0.559 0.554 80 0.570 0.570 0.570 0.570 0.570 0.570 0.570 0.569 0.567 0.565 0.565 90 0.569 0.569 0.569 0.569 0.570 0.571 0.571 0.571 0.571 0.570 0.569
100 0.569 0.569 0.570 0.570 0.571 0.572 0.572 0.573 0.573 0.573 0.573
Figure 17: CH4 (SR) – Fuel Utilization versus Part Load.
58
Table 13: CH4 (SR) – Turbine Inlet Temperature.
Turbine Inlet Temperature (K) – CH4 (IR)
Load
(%)
Altitude (ft) 0E+0 2E+3 4E+3 6E+3 8E+3 10E+3 12E+3 14E+3 16E+3 18E+3 20E+3
10 1085 1086 1087 1088 1089 1089 1090 1091 1091 1092 1092 20 1087 1087 1088 1089 1089 1090 1091 1091 1092 1092 1093 30 1088 1089 1090 1090 1091 1091 1092 1092 1093 1093 1093 40 1091 1091 1092 1092 1093 1093 1093 1093 1093 1093 1093 50 1093 1093 1093 1093 1093 1093 1093 1093 1093 1093 1093 60 1093 1093 1093 1093 1093 1093 1093 1093 1093 1093 1093 70 1093 1093 1093 1093 1093 1093 1093 1093 1093 1093 1093 80 1093 1093 1093 1093 1093 1093 1093 1093 1093 1093 1093 90 1093 1093 1093 1093 1093 1093 1093 1093 1093 1093 1093
100 1093 1093 1093 1093 1093 1093 1093 1093 1093 1093 1093
Figure 18: CH4 (SR) – Turbine Inlet Temperature versus Part Load.
59
Table 14: CH4 (SR) – Gas Turbine Shaft Speed.
Shaft Speed (kRPM) – CH4 (IR)
Load
(%)
Altitude (ft) 0E+0 2E+3 4E+3 6E+3 8E+3 10E+3 12E+3 14E+3 16E+3 18E+3 20E+3
10 55.0 55.0 55.0 55.0 55.0 55.0 55.0 55.0 55.0 55.0 55.0 20 55.0 55.0 55.0 55.0 55.0 55.0 55.0 55.0 55.0 55.0 55.0 30 55.0 55.0 55.0 55.0 55.0 55.0 55.0 55.0 55.0 56.5 60.6 40 55.0 55.0 55.0 55.0 55.0 55.2 57.8 60.8 63.7 67.2 70.8 50 61.0 61.3 62.8 64.8 66.7 69.0 71.4 73.6 75.3 77.0 79.4 60 78.0 77.7 78.3 79.4 80.4 81.5 82.8 84.3 85.3 86.5 88.1 70 91.5 90.7 91.1 91.7 92.3 93.0 93.4 94.4 94.7 95.4 96.5 80 103.5 102.5 102.5 102.5 102.4 102.4 102.4 102.8 102.9 102.9 103.0 90 113.4 112.1 112.0 112.1 111.7 111.4 111.3 111.7 111.3 111.1 111.2
100 124.4 122.8 122.3 122.2 121.7 121.6 121.5 121.9 121.4 120.8 120.8
Figure 19: CH4 (SR) – Gas Turbine Shaft Speed versus Part Load.
60
Table 15: CH4 (SR) – Compressor Mass Flow Rate.
Compressor Mass Flow Rate (kg/s) – CH4 (IR)
Load
(%)
Altitude (ft) 0E+0 2E+3 4E+3 6E+3 8E+3 10E+3 12E+3 14E+3 16E+3 18E+3 20E+3
10 0.042 0.040 0.037 0.035 0.033 0.031 0.029 0.027 0.025 0.024 0.022 20 0.042 0.040 0.037 0.035 0.033 0.031 0.029 0.027 0.025 0.024 0.022 30 0.043 0.040 0.038 0.035 0.033 0.031 0.029 0.027 0.026 0.024 0.024 40 0.043 0.040 0.038 0.036 0.033 0.032 0.031 0.030 0.029 0.028 0.027 50 0.047 0.044 0.042 0.041 0.039 0.037 0.036 0.035 0.033 0.032 0.031 60 0.057 0.053 0.051 0.049 0.046 0.044 0.042 0.041 0.039 0.037 0.035 70 0.068 0.064 0.060 0.058 0.054 0.052 0.049 0.047 0.045 0.042 0.041 80 0.081 0.076 0.071 0.068 0.064 0.060 0.057 0.054 0.051 0.048 0.046 90 0.095 0.088 0.083 0.079 0.074 0.070 0.066 0.062 0.058 0.055 0.052
100 0.110 0.102 0.096 0.091 0.085 0.080 0.075 0.071 0.066 0.062 0.058
Figure 20: CH4 (SR) – Compressor Mass Flow Rate versus Part Load.
61
Table 16: CH4 (SR) – Solid Oxide Fuel Cell Voltage.
SOFC Voltage (V) – CH4 (IR)
Load
(%)
Altitude (ft) 0E+0 2E+3 4E+3 6E+3 8E+3 10E+3 12E+3 14E+3 16E+3 18E+3 20E+3
10 0.927 0.927 0.927 0.927 0.927 0.926 0.926 0.925 0.924 0.924 0.923 20 0.857 0.860 0.862 0.863 0.865 0.866 0.867 0.868 0.869 0.871 0.871 30 0.794 0.800 0.803 0.806 0.810 0.813 0.816 0.818 0.821 0.825 0.830 40 0.737 0.744 0.750 0.754 0.760 0.764 0.770 0.776 0.782 0.789 0.795 50 0.687 0.697 0.705 0.712 0.720 0.727 0.735 0.741 0.749 0.757 0.764 60 0.647 0.658 0.667 0.675 0.685 0.693 0.702 0.709 0.718 0.727 0.736 70 0.609 0.621 0.632 0.641 0.652 0.661 0.671 0.680 0.689 0.700 0.709 80 0.573 0.587 0.598 0.609 0.620 0.631 0.641 0.651 0.662 0.673 0.683 90 0.538 0.554 0.566 0.578 0.590 0.602 0.614 0.624 0.636 0.648 0.659
100 0.506 0.522 0.535 0.548 0.562 0.574 0.587 0.598 0.611 0.624 0.636
Figure 21: CH4 (SR) – Solid Oxide Fuel Cell Voltage versus Part Load.
62
Table 17: CH4 (SR) – Solid Oxide Fuel Cell Power.
SOFC Power (kW) – CH4 (IR)
Load
(%)
Altitude (ft) 0E+0 2E+3 4E+3 6E+3 8E+3 10E+3 12E+3 14E+3 16E+3 18E+3 20E+3
10 4.18 3.97 3.79 3.63 3.45 3.29 3.12 2.98 2.82 2.66 2.52 20 7.74 7.36 7.04 6.75 6.43 6.14 5.86 5.60 5.31 5.02 4.76 30 10.76 10.27 9.85 9.47 9.04 8.65 8.26 7.91 7.52 7.13 6.80 40 13.31 12.74 12.25 11.81 11.30 10.84 10.40 10.01 9.55 9.10 8.69 50 15.52 14.91 14.40 13.93 13.39 12.90 12.40 11.95 11.44 10.90 10.43 60 17.53 16.90 16.35 15.86 15.28 14.76 14.22 13.73 13.16 12.57 12.05 70 19.24 18.61 18.06 17.56 16.97 16.43 15.86 15.34 14.73 14.11 13.55 80 20.68 20.08 19.55 19.05 18.46 17.90 17.32 16.79 16.17 15.52 14.92 90 21.87 21.32 20.82 20.34 19.76 19.21 18.64 18.11 17.47 16.81 16.20
100 22.83 22.33 21.87 21.43 20.89 20.37 19.81 19.29 18.66 17.99 17.37
Figure 22: CH4 (SR) – Solid Oxide Fuel Cell Power versus Part Load.
63
Table 18: CH4 (SR) – Gas Turbine Power.
GT Power (kW) – CH4 (IR)
Load
(%)
Altitude (ft) 0E+0 2E+3 4E+3 6E+3 8E+3 10E+3 12E+3 14E+3 16E+3 18E+3 20E+3
10 1.68 1.66 1.63 1.60 1.56 1.52 1.48 1.44 1.40 1.35 1.30 20 1.79 1.77 1.73 1.70 1.65 1.61 1.56 1.52 1.47 1.42 1.37 30 1.91 1.87 1.83 1.79 1.74 1.70 1.65 1.60 1.54 1.52 1.56 40 2.03 1.98 1.93 1.89 1.84 1.79 1.80 1.82 1.82 1.84 1.87 50 2.31 2.27 2.25 2.25 2.23 2.23 2.22 2.23 2.23 2.21 2.22 60 2.91 2.85 2.81 2.80 2.76 2.74 2.72 2.71 2.68 2.64 2.63 70 3.54 3.46 3.42 3.40 3.34 3.31 3.26 3.24 3.18 3.13 3.10 80 4.17 4.09 4.05 4.02 3.95 3.90 3.83 3.79 3.72 3.64 3.56 90 4.73 4.67 4.64 4.62 4.55 4.48 4.41 4.36 4.26 4.16 4.08
100 5.13 5.13 5.12 5.12 5.06 5.01 4.95 4.89 4.79 4.67 4.58
Figure 23: CH4 (SR) – Gas Turbine Power versus Part Load.
64
Table 19: JP8 (SR) – System Load.
Part Load (A) Calculations – JP8 (SR)
Load
(%)
Altitude (ft) 0E+0 2E+3 4E+3 6E+3 8E+3 10E+3 12E+3 14E+3 16E+3 18E+3 20E+3
10 21.2 20.2 19.3 18.5 17.6 16.8 16.0 15.2 14.4 13.6 12.9 20 42.4 40.4 38.6 37.0 35.2 33.6 32.0 30.4 28.8 27.2 25.8 30 63.6 60.6 57.9 55.5 52.8 50.4 48.0 45.6 43.2 40.8 38.7 40 84.8 80.8 77.2 74.0 70.4 67.2 64.0 60.8 57.6 54.4 51.6 50 106.0 101.0 96.5 92.5 88.0 84.0 80.0 76.0 72.0 68.0 64.5 60 127.2 121.2 115.8 111.0 105.6 100.8 96.0 91.2 86.4 81.6 77.4 70 148.4 141.4 135.1 129.5 123.2 117.6 112.0 106.4 100.8 95.2 90.3 80 169.6 161.6 154.4 148.0 140.8 134.4 128.0 121.6 115.2 108.8 103.2 90 190.8 181.8 173.7 166.5 158.4 151.2 144.0 136.8 129.6 122.4 116.1
100 212.0 202.0 193.0 185.0 176.0 168.0 160.0 152.0 144.0 136.0 129.0
Figure 24: JP8 (SR) – System Load versus Part Load.
65
Table 20: JP8 (SR) – Fuel Utilization.
Fuel Utilization ( – JP8 (SR)
Loa
d
(%)
Altitude (ft) 0E+0 2E+3 4E+3 6E+3 8E+3 10E+3 12E+3 14E+
3
16E+3 18E+3 20E+3
10 0.21 0.206 0.207 0.209 0.21 0.210
5
0.212 0.21
3
0.213 0.213 0.214 20 0.34
5
0.3440
5
0.345 0.347 0.34
9
0.350
5
0.352 0.35
3
0.353 0.353 0.355 30 0.44
3
0.4420
7
0.443 0.446 0.44
8
0.449 0.450
2
0.45
2
0.452 0.440
8
0.430
5
40 0.51
6
0.516 0.516
8
0.519 0.51
8
0.513 0.508 0.5 0.49 0.486 0.475 50 0.55 0.545 0.542 0.539 0.53
5
0.532 0.528 0.52
2
0.517
5
0.51 0.506 60 0.55
4
0.55 0.547 0.546
2
0.54
4
0.541 0.54 0.53
3
0.532 0.528 0.524 70 0.55
4
0.55 0.547 0.546
2
0.54
5
0.545 0.545 0.54
4
0.54 0.534
5
0.534
5
80 0.55
4
0.55 0.548 0.548 0.54
7
0.547 0.548 0.54
8
0.547 0.545 0.543 90 0.55
4
0.55 0.549 0.549
2
0.55 0.55 0.55 0.55 0.55 0.547 0.547 100 0.55
4
0.554 0.554 0.554 0.55
6
0.556 0.556 0.55
6
0.556 0.555 0.555
Figure 25: JP8 (SR) – Fuel Utilization versus Part Load.
66
Table 21: JP8 (SR) – Turbine Inlet Temperature.
Turbine Inlet Temperature (K) – JP8 (SR)
Load
(%)
Altitude (ft) 0E+0 2E+3 4E+3 6E+3 8E+3 10E+3 12E+3 14E+3 16E+3 18E+3 20E+3
10 1085 1086 1087 1088 1089 1089 1090 1091 1091 1092 1092 20 1087 1087 1088 1089 1090 1090 1091 1091 1092 1092 1093 30 1089 1089 1090 1091 1091 1092 1092 1093 1093 1093 1093 40 1092 1092 1092 1093 1093 1093 1093 1093 1093 1093 1093 50 1093 1093 1093 1093 1093 1093 1093 1093 1093 1093 1093 60 1093 1093 1093 1093 1093 1093 1093 1093 1093 1093 1093 70 1093 1093 1093 1093 1093 1093 1093 1093 1093 1093 1093 80 1093 1093 1093 1093 1093 1093 1093 1093 1093 1093 1093 90 1093 1093 1093 1093 1093 1093 1093 1093 1093 1093 1093
100 1094 1093 1093 1093 1093 1093 1093 1093 1093 1093 1093
Figure 26: JP8 (SR) – Turbine Inlet Temperature versus Part Load.
67
Table 22: JP8 (SR) – Gas Turbine Shaft Speed.
Shaft Speed (kRPM) – JP8 (SR)
Load
(%)
Altitude (ft) 0E+0 2E+3 4E+3 6E+3 8E+3 10E+3 12E+3 14E+3 16E+3 18E+3 20E+3
10 55.0 55.0 55.0 55.0 55.0 55.0 55.0 55.0 55.0 55.0 55.0 20 55.0 55.0 55.0 55.0 55.0 55.0 55.0 55.0 55.0 55.0 55.0 30 55.0 55.0 55.0 55.0 55.0 55.0 55.0 55.0 55.3 58.9 63.3 40 55.0 55.0 55.0 55.0 56.1 58.3 60.6 63.9 67.8 70.2 73.3 50 63.0 64.6 66.6 68.7 71.1 73.0 74.5 76.4 77.9 80.1 81.8 60 79.7 80.4 81.7 82.7 83.7 85.0 85.9 87.7 88.2 89.4 90.7 70 93.4 93.9 95.0 95.5 96.1 96.2 96.6 97.0 97.7 98.5 98.7 80 104.8 104.9 105.3 105.4 105.5 105.5 105.4 105.3 105.3 105.5 106.1 90 114.8 114.9 115.1 115.2 114.9 114.8 114.8 114.6 114.2 114.6 114.7
100 125.0 125.0 125.0 125.0 125.0 125.0 125.0 125.0 124.6 124.8 125.0
Figure 27: JP8 (SR) – Gas Turbine Shaft Speed versus Part Load.
68
Table 23: JP8 (SR) – Compressor Mass Flow Rate.
Compressor Mass Flow Rate (kg/s) – JP8 (SR)
Load
(%)
Altitude (ft) 0E+0 2E+3 4E+3 6E+3 8E+3 10E+3 12E+3 14E+3 16E+3 18E+3 20E+3
10 0.042 0.040 0.037 0.035 0.033 0.031 0.029 0.027 0.025 0.024 0.022 20 0.043 0.040 0.038 0.036 0.033 0.031 0.029 0.027 0.026 0.024 0.022 30 0.043 0.041 0.038 0.036 0.034 0.032 0.030 0.028 0.026 0.026 0.025 40 0.043 0.041 0.038 0.036 0.034 0.033 0.032 0.031 0.030 0.029 0.029 50 0.048 0.046 0.044 0.043 0.041 0.039 0.038 0.037 0.035 0.034 0.033 60 0.059 0.056 0.054 0.051 0.049 0.047 0.045 0.043 0.041 0.039 0.037 70 0.071 0.067 0.064 0.061 0.058 0.055 0.052 0.049 0.047 0.045 0.043 80 0.083 0.079 0.076 0.072 0.068 0.064 0.061 0.057 0.054 0.051 0.048 90 0.098 0.093 0.088 0.083 0.078 0.074 0.070 0.066 0.062 0.058 0.055
100 0.112 0.106 0.100 0.094 0.089 0.084 0.079 0.074 0.069 0.065 0.061
Figure 28: JP8 (SR) – Compressor Mass Flow Rate versus Part Load.
69
Table 24: JP8 (SR) – Solid Oxide Fuel Cell Voltage.
SOFC Voltage (V) – JP8 (SR)
Load
(%)
Altitude (ft) 0E+0 2E+3 4E+3 6E+3 8E+3 10E+3 12E+3 14E+3 16E+3 18E+3 20E+3
10 0.921 0.922 0.921 0.921 0.921 0.920 0.920 0.919 0.919 0.919 0.918 20 0.853 0.855 0.857 0.858 0.860 0.861 0.863 0.864 0.865 0.866 0.867 30 0.791 0.796 0.799 0.802 0.806 0.809 0.812 0.814 0.818 0.823 0.828 40 0.734 0.741 0.746 0.750 0.756 0.762 0.768 0.774 0.781 0.787 0.794 50 0.686 0.695 0.703 0.710 0.718 0.725 0.733 0.740 0.748 0.756 0.762 60 0.646 0.656 0.666 0.674 0.683 0.691 0.699 0.709 0.717 0.726 0.734 70 0.608 0.620 0.631 0.640 0.651 0.660 0.669 0.678 0.689 0.699 0.707 80 0.572 0.586 0.597 0.607 0.619 0.629 0.640 0.650 0.661 0.672 0.682 90 0.538 0.553 0.565 0.576 0.589 0.600 0.612 0.623 0.635 0.648 0.658
100 0.507 0.521 0.534 0.546 0.559 0.572 0.584 0.597 0.610 0.623 0.635
Figure 29: JP8 (SR) – Solid Oxide Fuel Cell Voltage versus Part Load.
70
Table 25: JP8 (SR) – Solid Oxide Fuel Cell Power.
SOFC Power (kW) – JP8 (SR)
Load
(%)
Altitude (ft) 0E+0 2E+3 4E+3 6E+3 8E+3 10E+3 12E+3 14E+3 16E+3 18E+3 20E+3
10 3.90 3.72 3.56 3.41 3.24 3.09 2.94 2.79 2.65 2.50 2.37 20 7.23 6.91 6.62 6.35 6.05 5.79 5.52 5.25 4.98 4.71 4.47 30 10.06 9.64 9.26 8.90 8.51 8.15 7.79 7.43 7.06 6.72 6.41 40 12.45 11.97 11.52 11.11 10.65 10.24 9.83 9.42 9.00 8.57 8.19 50 14.54 14.04 13.57 13.14 12.64 12.18 11.72 11.25 10.77 10.28 9.83 60 16.43 15.91 15.42 14.95 14.42 13.94 13.43 12.93 12.39 11.85 11.36 70 18.05 17.54 17.05 16.58 16.03 15.51 14.98 14.43 13.88 13.31 12.77 80 19.41 18.92 18.44 17.98 17.43 16.92 16.37 15.81 15.23 14.62 14.07 90 20.53 20.09 19.64 19.19 18.65 18.15 17.62 17.05 16.46 15.86 15.28
100 21.49 21.05 20.62 20.21 19.69 19.21 18.70 18.15 17.56 16.95 16.37
Figure 30: JP8 (SR) – Solid Oxide Fuel Cell Power versus Part Load.
71
Table 26: JP8 (SR) – Gas Turbine Power.
GT Power (kW) – JP8 (SR)
Load
(%)
Altitude (ft) 0E+0 2E+3 4E+3 6E+3 8E+3 10E+3 12E+3 14E+3 16E+3 18E+3 20E+3
10 1.69 1.68 1.65 1.62 1.58 1.54 1.50 1.45 1.41 1.36 1.32 20 1.81 1.79 1.75 1.72 1.67 1.63 1.58 1.53 1.49 1.44 1.38 30 1.93 1.90 1.86 1.82 1.76 1.72 1.67 1.62 1.57 1.60 1.63 40 2.05 2.01 1.96 1.92 1.89 1.89 1.89 1.91 1.94 1.93 1.97 50 2.39 2.38 2.38 2.38 2.37 2.36 2.36 2.36 2.35 2.35 2.34 60 3.00 2.98 2.97 2.96 2.93 2.91 2.88 2.88 2.83 2.79 2.77 70 3.65 3.64 3.63 3.61 3.56 3.51 3.46 3.40 3.36 3.33 3.26 80 4.27 4.27 4.25 4.23 4.18 4.13 4.05 3.98 3.90 3.82 3.76 90 4.82 4.83 4.82 4.81 4.74 4.70 4.63 4.56 4.46 4.39 4.30
100 5.21 5.23 5.23 5.25 5.19 5.16 5.11 5.04 4.95 4.85 4.75
Figure 31: JP8 (SR) – Gas Turbine Power versus Part Load.
72
Table 27: H2 – System Load.
Part Load (A) Calculations – H2
Load
(%)
Altitude (ft) 0E+0 2E+3 4E+3 6E+3 8E+3 10E+3 12E+3 14E+3 16E+3 18E+3 20E+3
10 23.0 22.0 21.0 20.1 19.2 18.3 17.4 16.6 15.8 14.9 14.1 20 46.0 44.0 42.0 40.2 38.4 36.6 34.8 33.2 31.6 29.8 28.2 30 69.0 66.0 63.0 60.3 57.6 54.9 52.2 49.8 47.4 44.7 42.3 40 92.0 88.0 84.0 80.4 76.8 73.2 69.6 66.4 63.2 59.6 56.4 50 115.0 110.0 105.0 100.5 96.0 91.5 87.0 83.0 79.0 74.5 70.5 60 138.0 132.0 126.0 120.6 115.2 109.8 104.4 99.6 94.8 89.4 84.6 70 161.0 154.0 147.0 140.7 134.4 128.1 121.8 116.2 110.6 104.3 98.7 80 184.0 176.0 168.0 160.8 153.6 146.4 139.2 132.8 126.4 119.2 112.8 90 207.0 198.0 189.0 180.9 172.8 164.7 156.6 149.4 142.2 134.1 126.9
100 230.0 220.0 210.0 201.0 192.0 183.0 174.0 166.0 158.0 149.0 141.0
Figure 32: H2 – System Load versus Part Load.
73
Table 28: H2 – Fuel Utilization.
Fuel Utilization ( – H2
Load
(%)
Altitude (ft) 0E+0 2E+3 4E+3 6E+3 8E+3 10E+3 12E+3 14E+3 16E+3 18E+3 20E+3
10 0.196 0.196 0.197 0.198 0.199 0.200 0.201 0.202 0.203 0.203 0.204 20 0.328 0.328 0.330 0.331 0.334 0.335 0.336 0.338 0.339 0.339 0.334 30 0.423 0.424 0.425 0.427 0.430 0.431 0.432 0.426 0.418 0.409 0.400 40 0.490 0.489 0.485 0.481 0.476 0.471 0.466 0.460 0.454 0.447 0.440 50 0.500 0.496 0.496 0.493 0.491 0.487 0.483 0.479 0.474 0.469 0.463 60 0.502 0.501 0.501 0.499 0.497 0.495 0.492 0.489 0.486 0.483 0.480 70 0.502 0.502 0.502 0.502 0.502 0.500 0.498 0.496 0.494 0.492 0.490 80 0.503 0.503 0.503 0.503 0.503 0.503 0.503 0.503 0.500 0.498 0.496 90 0.506 0.506 0.506 0.506 0.506 0.506 0.506 0.507 0.507 0.506 0.506
100 0.529 0.528 0.529 0.530 0.531 0.531 0.531 0.532 0.533 0.532 0.532
Figure 33: H2 – Fuel Utilization versus Part Load.
74
Table 29: H2 – Turbine Inlet Temperature.
Turbine Inlet Temperature (K) – H2
Load
(%)
Altitude (ft) 0E+0 2E+3 4E+3 6E+3 8E+3 10E+3 12E+3 14E+3 16E+3 18E+3 20E+3
10 1085 1086 1087 1088 1089 1089 1090 1091 1091 1092 1092 20 1087 1088 1089 1089 1090 1091 1091 1092 1092 1093 1093 30 1090 1090 1091 1091 1092 1092 1093 1093 1093 1093 1093 40 1093 1093 1093 1093 1093 1093 1093 1093 1093 1093 1093 50 1093 1093 1093 1093 1093 1093 1093 1093 1093 1093 1093 60 1093 1093 1093 1093 1093 1093 1093 1093 1093 1093 1093 70 1093 1093 1093 1093 1093 1093 1093 1093 1093 1093 1093 80 1093 1093 1093 1093 1093 1093 1093 1093 1093 1093 1093 90 1093 1093 1093 1093 1093 1093 1093 1093 1093 1093 1093
100 1098 1098 1098 1097 1098 1097 1097 1097 1097 1096 1096
Figure 34: H2 – Turbine Inlet Temperature versus Part Load.
75
Table 30: H2 – Gas Turbine Shaft Speed.
Shaft Speed (kRPM) – H2
Load
(%)
Altitude (ft) 0E+0 2E+3 4E+3 6E+3 8E+3 10E+3 12E+3 14E+3 16E+3 18E+3 20E+3
10 55.0 55.0 55.0 55.0 55.0 55.0 55.0 55.0 55.0 55.0 55.0 20 55.0 55.0 55.0 55.0 55.0 55.0 55.0 55.0 55.0 55.0 57.1 30 55.0 55.0 55.0 55.0 55.0 55.0 55.0 57.7 61.1 64.7 68.8 40 56.3 57.2 59.1 61.1 64.1 66.5 69.1 72.1 74.3 76.3 78.7 50 74.6 75.9 76.6 77.8 79.3 80.7 82.2 84.0 85.8 87.1 89.0 60 89.6 90.0 90.4 91.3 92.5 93.3 94.1 95.1 96.3 96.8 97.4 70 102.8 102.6 102.7 102.7 103.1 103.4 103.7 104.3 104.8 105.0 105.5 80 113.2 112.9 112.9 112.9 113.4 113.3 113.2 113.4 114.1 114.3 114.7 90 124.3 123.8 123.8 124.1 125.0 124.9 124.8 124.9 125.0 125.0 125.0
100 125.0 125.0 125.0 125.0 125.0 125.0 125.0 125.0 125.0 125.0 125.0
Figure 35: H2 – Gas Turbine Speed versus Part Load.
76
Table 31: H2 – Compressor Mass Flow Rate.
Compressor Mass Flow Rate (kg/s) – H2
Load
(%)
Altitude (ft) 0E+0 2E+3 4E+3 6E+3 8E+3 10E+3 12E+3 14E+3 16E+3 18E+3 20E+3
10 0.041 0.038 0.036 0.034 0.032 0.030 0.028 0.026 0.025 0.023 0.021 20 0.041 0.039 0.036 0.034 0.032 0.030 0.028 0.026 0.025 0.023 0.022 30 0.041 0.039 0.036 0.034 0.032 0.030 0.028 0.027 0.027 0.026 0.025 40 0.042 0.040 0.038 0.037 0.036 0.035 0.033 0.032 0.031 0.030 0.029 50 0.052 0.050 0.047 0.045 0.043 0.042 0.040 0.038 0.037 0.035 0.034 60 0.063 0.060 0.057 0.055 0.052 0.050 0.047 0.045 0.043 0.041 0.039 70 0.076 0.072 0.068 0.065 0.062 0.059 0.056 0.053 0.051 0.048 0.045 80 0.091 0.086 0.081 0.077 0.073 0.068 0.064 0.061 0.058 0.055 0.052 90 0.106 0.100 0.094 0.089 0.084 0.079 0.075 0.070 0.066 0.062 0.058
100 0.107 0.101 0.095 0.090 0.084 0.079 0.075 0.070 0.066 0.062 0.058
Figure 36: H2 – Compressor Mass Flow Rate versus Part Load.
77
Table 32: H2 – Solid Oxide Fuel Cell Voltage.
SOFC Voltage (V) – H2
Load
(%)
Altitude (ft) 0E+0 2E+3 4E+3 6E+3 8E+3 10E+3 12E+3 14E+3 16E+3 18E+3 20E+3
10 0.958 0.958 0.958 0.958 0.958 0.957 0.957 0.956 0.956 0.956 0.955 20 0.876 0.879 0.881 0.883 0.884 0.886 0.887 0.888 0.889 0.891 0.894 30 0.808 0.812 0.817 0.820 0.823 0.827 0.830 0.835 0.840 0.846 0.851 40 0.748 0.755 0.762 0.768 0.775 0.781 0.788 0.794 0.801 0.808 0.814 50 0.702 0.711 0.719 0.727 0.735 0.743 0.751 0.758 0.766 0.774 0.782 60 0.661 0.670 0.680 0.689 0.698 0.707 0.717 0.725 0.734 0.743 0.752 70 0.622 0.632 0.643 0.653 0.663 0.674 0.684 0.694 0.703 0.714 0.724 80 0.584 0.596 0.608 0.619 0.630 0.642 0.653 0.663 0.674 0.687 0.698 90 0.549 0.562 0.575 0.587 0.599 0.612 0.624 0.635 0.647 0.660 0.672
100 0.516 0.529 0.542 0.554 0.567 0.579 0.592 0.604 0.616 0.629 0.642
Figure 37: H2 – Solid Oxide Fuel Cell Voltage versus Part Load.
78
Table 33: H2 – Solid Oxide Fuel Cell Power.
SOFC Power (kW) – H2
Load
(%)
Altitude (ft) 0E+0 2E+3 4E+3 6E+3 8E+3 10E+3 12E+3 14E+3 16E+3 18E+3 20E+3
10 3.97 3.79 3.62 3.47 3.31 3.15 3.00 2.86 2.72 2.56 2.42 20 7.26 6.96 6.66 6.39 6.11 5.83 5.56 5.31 5.06 4.78 4.54 30 10.03 9.65 9.26 8.90 8.53 8.17 7.80 7.48 7.16 6.80 6.48 40 12.39 11.95 11.52 11.12 10.71 10.29 9.87 9.49 9.11 8.67 8.27 50 14.54 14.08 13.60 13.15 12.70 12.23 11.76 11.33 10.89 10.38 9.93 60 16.41 15.93 15.42 14.96 14.48 13.98 13.47 13.00 12.52 11.96 11.45 70 18.01 17.53 17.02 16.54 16.04 15.53 15.00 14.51 14.00 13.41 12.86 80 19.35 18.89 18.39 17.93 17.43 16.91 16.37 15.86 15.34 14.73 14.16 90 20.45 20.02 19.56 19.11 18.64 18.13 17.59 17.08 16.55 15.93 15.34
100 21.34 20.94 20.49 20.05 19.58 19.08 18.55 18.04 17.51 16.88 16.29
Figure 38: H2 – Solid Oxide Fuel Cell Power versus Part Load.
79
Table 34: H2 – Gas Turbine Power.
GT Power (kW) – H2
Load
(%)
Altitude (ft) 0E+0 2E+3 4E+3 6E+3 8E+3 10E+3 12E+3 14E+3 16E+3 18E+3 20E+3
10 1.58 1.56 1.54 1.51 1.47 1.44 1.40 1.37 1.33 1.28 1.24 20 1.66 1.64 1.61 1.58 1.54 1.51 1.47 1.42 1.38 1.33 1.33 30 1.75 1.73 1.69 1.66 1.61 1.57 1.53 1.54 1.57 1.59 1.62 40 1.88 1.87 1.87 1.88 1.90 1.90 1.91 1.93 1.95 1.95 1.96 50 2.40 2.41 2.39 2.39 2.39 2.39 2.38 2.39 2.40 2.38 2.38 60 2.99 2.98 2.96 2.96 2.95 2.93 2.91 2.91 2.89 2.85 2.82 70 3.57 3.57 3.55 3.53 3.50 3.48 3.45 3.44 3.41 3.34 3.29 80 4.06 4.08 4.07 4.07 4.05 4.02 3.97 3.93 3.92 3.85 3.79 90 4.37 4.44 4.46 4.49 4.49 4.47 4.44 4.40 4.36 4.28 4.19
100 4.63 4.68 4.69 4.70 4.68 4.65 4.61 4.56 4.49 4.40 4.31
Figure 39: H2 – Gas Turbine Power versus Part Load.
80
Table 35: CH4 (POX) – System Load.
Part Load (A) Calculations – CH4 (POX)
Load
(%)
Altitude (ft) 0E+0 2E+3 4E+3 6E+3 8E+3 10E+3 12E+3 14E+3 16E+3 18E+3 20E+3
10 21.3 20.4 19.4 18.6 17.7 16.9 16.1 15.3 14.5 13.7 12.9 20 42.6 40.8 38.8 37.2 35.4 33.8 32.2 30.6 29.0 27.4 25.8 30 63.9 61.2 58.2 55.8 53.1 50.7 48.3 45.9 43.5 41.1 38.7 40 85.2 81.6 77.6 74.4 70.8 67.6 64.4 61.2 58.0 54.8 51.6 50 106.5 102.0 97.0 93.0 88.5 84.5 80.5 76.5 72.5 68.5 64.5 60 127.8 122.4 116.4 111.6 106.2 101.4 96.6 91.8 87.0 82.2 77.4 70 149.1 142.8 135.8 130.2 123.9 118.3 112.7 107.1 101.5 95.9 90.3 80 170.4 163.2 155.2 148.8 141.6 135.2 128.8 122.4 116.0 109.6 103.2 90 191.7 183.6 174.6 167.4 159.3 152.1 144.9 137.7 130.5 123.3 116.1
100 213.0 204.0 194.0 186.0 177.0 169.0 161.0 153.0 145.0 137.0 129.0
Figure 40: CH4 (POX) – System Load versus Part Load.
81
Table 36: CH4 (POX) – Fuel Utilization.
Fuel Utilization ( – CH4 (POX)
Load
(%)
Altitude (ft) 0E+0 2E+3 4E+3 6E+3 8E+3 10E+3 12E+3 14E+3 16E+3 18E+3 20E+3
10 0.191 0.192 0.192 0.193 0.194 0.195 0.196 0.197 0.197 0.198 0.197 20 0.322 0.323 0.324 0.325 0.327 0.328 0.330 0.331 0.331 0.332 0.331 30 0.418 0.419 0.419 0.421 0.423 0.425 0.426 0.427 0.421 0.412 0.402 40 0.490 0.491 0.492 0.490 0.485 0.480 0.474 0.468 0.457 0.451 0.445 50 0.514 0.511 0.508 0.505 0.502 0.497 0.494 0.489 0.484 0.478 0.471 60 0.518 0.517 0.515 0.513 0.511 0.508 0.505 0.500 0.497 0.495 0.488 70 0.519 0.519 0.519 0.518 0.517 0.516 0.513 0.510 0.508 0.505 0.501 80 0.520 0.520 0.520 0.520 0.520 0.520 0.519 0.516 0.515 0.512 0.509 90 0.522 0.522 0.522 0.522 0.522 0.522 0.522 0.522 0.520 0.518 0.516
100 0.529 0.529 0.529 0.529 0.530 0.530 0.530 0.530 0.529 0.529 0.528
Figure 41: CH4 (POX) – Fuel Utilization versus Part Load.
82
Table 37: CH4 (POX) – Turbine Inlet Temperature.
Turbine Inlet Temperature (K) – CH4 (POX)
Load
(%)
Altitude (ft) 0E+0 2E+3 4E+3 6E+3 8E+3 10E+3 12E+3 14E+3 16E+3 18E+3 20E+3
10 1085 1086 1087 1088 1088 1089 1090 1090 1091 1092 1092 20 1087 1087 1088 1089 1090 1090 1091 1091 1092 1092 1093 30 1089 1090 1090 1091 1091 1092 1092 1093 1093 1093 1093 40 1092 1092 1093 1093 1093 1093 1093 1093 1093 1093 1093 50 1093 1093 1093 1093 1093 1093 1093 1093 1093 1093 1093 60 1093 1093 1093 1093 1093 1093 1093 1093 1093 1093 1093 70 1093 1093 1093 1093 1093 1093 1093 1093 1093 1093 1093 80 1093 1093 1093 1093 1093 1093 1093 1093 1093 1093 1093 90 1093 1093 1093 1093 1093 1093 1093 1093 1093 1093 1093
100 1094 1094 1094 1094 1094 1094 1094 1094 1094 1094 1094
Figure 42: CH4 (POX) – Turbine Inlet Temperature versus Part Load.
83
Table 38: CH4 (POX) – Gas Turbine Shaft Speed.
Shaft Speed (kRPM) – CH4 (POX)
Load
(%)
Altitude (ft) 0E+0 2E+3 4E+3 6E+3 8E+3 10E+3 12E+3 14E+3 16E+3 18E+3 20E+3
10 55.0 55.0 55.0 55.0 55.0 55.0 55.0 55.0 55.0 55.0 55.0 20 55.0 55.0 55.0 55.0 55.0 55.0 55.0 55.0 55.0 55.0 55.1 30 55.0 55.0 55.0 55.0 55.0 55.0 55.0 55.0 57.3 60.7 64.6 40 55.0 55.0 55.0 56.3 58.5 60.8 63.7 66.7 70.9 72.8 74.7 50 66.6 68.4 69.9 72.2 73.9 75.7 77.1 78.9 80.6 82.4 84.1 60 82.7 83.3 84.0 85.2 86.3 87.5 88.7 90.2 91.1 91.7 92.9 70 96.2 96.2 96.1 96.9 97.1 97.8 98.7 99.3 99.5 100.0 100.4 80 106.8 106.6 106.3 106.4 106.4 106.5 106.9 107.4 107.5 108.0 108.3 90 116.7 116.5 116.1 116.2 116.1 116.1 116.1 116.1 116.3 116.4 116.6
100 125.0 125.0 125.0 125.0 125.0 125.0 125.0 125.0 125.0 125.0 125.0
Figure 43: CH4 (POX) – Gas Turbine Shaft Speed versus Part Load.
84
Table 39: CH4 (POX) – Compressor Mass Flow Rate.
Compressor Mass Flow Rate (kg/s) – CH4 (POX)
Load
(%)
Altitude (ft) 0E+0 2E+3 4E+3 6E+3 8E+3 10E+3 12E+3 14E+3 16E+3 18E+3 20E+3
10 0.042 0.040 0.037 0.035 0.033 0.031 0.029 0.027 0.025 0.024 0.022 20 0.043 0.040 0.038 0.036 0.033 0.031 0.029 0.027 0.026 0.024 0.022 30 0.043 0.040 0.038 0.036 0.034 0.031 0.030 0.028 0.027 0.026 0.025 40 0.043 0.041 0.038 0.037 0.035 0.034 0.033 0.032 0.031 0.030 0.029 50 0.050 0.048 0.046 0.044 0.042 0.041 0.039 0.038 0.036 0.035 0.034 60 0.061 0.058 0.055 0.053 0.050 0.048 0.046 0.044 0.042 0.040 0.038 70 0.073 0.069 0.065 0.062 0.059 0.056 0.054 0.051 0.049 0.046 0.044 80 0.086 0.082 0.077 0.073 0.069 0.065 0.062 0.059 0.056 0.053 0.050 90 0.100 0.095 0.089 0.084 0.080 0.075 0.071 0.067 0.063 0.060 0.056
100 0.112 0.106 0.100 0.094 0.089 0.084 0.079 0.074 0.070 0.065 0.061
Figure 44: CH4 (POX) – Compressor Mass Flow Rate versus Part Load.
85
Table 40: CH4 (POX) – Solid Oxide Fuel Cell Voltage.
SOFC Voltage (V) – CH4 (POX)
Load
(%)
Altitude (ft) 0E+0 2E+3 4E+3 6E+3 8E+3 10E+3 12E+3 14E+3 16E+3 18E+3 20E+3
10 0.923 0.923 0.923 0.922 0.922 0.922 0.921 0.921 0.920 0.920 0.919 20 0.855 0.857 0.859 0.861 0.862 0.864 0.865 0.866 0.867 0.869 0.870 30 0.794 0.798 0.802 0.805 0.809 0.812 0.814 0.817 0.822 0.827 0.832 40 0.738 0.744 0.750 0.755 0.761 0.767 0.773 0.779 0.786 0.793 0.799 50 0.693 0.701 0.709 0.716 0.724 0.731 0.738 0.746 0.753 0.761 0.769 60 0.653 0.662 0.672 0.680 0.689 0.697 0.706 0.715 0.723 0.731 0.741 70 0.616 0.626 0.637 0.646 0.656 0.665 0.675 0.685 0.694 0.704 0.714 80 0.581 0.592 0.604 0.614 0.625 0.635 0.646 0.656 0.667 0.678 0.689 90 0.547 0.559 0.572 0.583 0.596 0.607 0.618 0.629 0.641 0.653 0.666
100 0.516 0.528 0.542 0.554 0.567 0.579 0.591 0.603 0.616 0.629 0.642
Figure 45: CH4 (POX) – Solid Oxide Fuel Cell Voltage versus Part Load.
86
Table 41: CH4 (POX) – Solid Oxide Fuel Cell Power.
SOFC Power (kW) – CH4 (POX)
Load
(%)
Altitude (ft) 0E+0 2E+3 4E+3 6E+3 8E+3 10E+3 12E+3 14E+3 16E+3 18E+3 20E+3
10 3.54 3.39 3.22 3.09 2.94 2.80 2.67 2.54 2.40 2.27 2.14 20 6.56 6.29 6.00 5.76 5.50 5.25 5.01 4.77 4.53 4.28 4.04 30 9.14 8.79 8.41 8.09 7.73 7.41 7.08 6.75 6.43 6.12 5.80 40 11.32 10.92 10.47 10.11 9.70 9.33 8.96 8.58 8.21 7.82 7.42 50 13.28 12.86 12.38 11.99 11.53 11.12 10.70 10.27 9.83 9.38 8.92 60 15.03 14.59 14.08 13.66 13.17 12.73 12.27 11.81 11.33 10.82 10.32 70 16.54 16.09 15.57 15.14 14.63 14.17 13.69 13.20 12.69 12.16 11.61 80 17.82 17.38 16.87 16.44 15.93 15.46 14.97 14.46 13.93 13.38 12.81 90 18.89 18.48 17.99 17.57 17.08 16.61 16.12 15.60 15.06 14.50 13.91
100 19.77 19.39 18.93 18.54 18.06 17.60 17.12 16.61 16.07 15.50 14.90
Figure 46: CH4 (POX) – Solid Oxide Fuel Cell Power versus Part Load.
87
Table 42: CH4 (POX) – Gas Turbine Power.
GT Power (kW) – CH4 (POX)
Load
(%)
Altitude (ft) 0E+0 2E+3 4E+3 6E+3 8E+3 10E+3 12E+3 14E+3 16E+3 18E+3 20E+3
10 1.70 1.67 1.64 1.61 1.57 1.53 1.49 1.45 1.41 1.36 1.31 20 1.80 1.77 1.74 1.70 1.66 1.62 1.57 1.52 1.48 1.42 1.38 30 1.91 1.88 1.83 1.80 1.74 1.70 1.65 1.60 1.60 1.62 1.65 40 2.02 1.98 1.93 1.92 1.92 1.93 1.94 1.96 2.00 1.99 1.99 50 2.44 2.44 2.43 2.43 2.42 2.43 2.42 2.42 2.41 2.40 2.39 60 3.05 3.04 3.01 3.00 2.98 2.97 2.95 2.95 2.91 2.86 2.84 70 3.69 3.67 3.61 3.60 3.56 3.52 3.50 3.47 3.42 3.36 3.31 80 4.28 4.27 4.22 4.20 4.14 4.10 4.06 4.02 3.94 3.88 3.81 90 4.77 4.78 4.75 4.75 4.70 4.66 4.61 4.54 4.47 4.39 4.30
100 5.09 5.13 5.12 5.14 5.10 5.07 5.02 4.96 4.89 4.78 4.67
Figure 47: CH4 (POX) – Gas Turbine Power versus Part Load.
88
Table 43: C3H8 (POX) – System Load.
Part Load (A) Calculations – C3H8 (POX)
Load
(%)
Altitude (ft) 0E+0 2E+3 4E+3 6E+3 8E+3 10E+3 12E+3 14E+3 16E+3 18E+3 20E+3
10 21.0 20.2 19.3 18.4 17.5 16.7 15.9 15.1 14.4 13.6 12.8 20 42.0 40.4 38.6 36.8 35.0 33.4 31.8 30.2 28.8 27.2 25.6 30 63.0 60.6 57.9 55.2 52.5 50.1 47.7 45.3 43.2 40.8 38.4 40 84.0 80.8 77.2 73.6 70.0 66.8 63.6 60.4 57.6 54.4 51.2 50 105.0 101.0 96.5 92.0 87.5 83.5 79.5 75.5 72.0 68.0 64.0 60 126.0 121.2 115.8 110.4 105.0 100.2 95.4 90.6 86.4 81.6 76.8 70 147.0 141.4 135.1 128.8 122.5 116.9 111.3 105.7 100.8 95.2 89.6 80 168.0 161.6 154.4 147.2 140.0 133.6 127.2 120.8 115.2 108.8 102.4 90 189.0 181.8 173.7 165.6 157.5 150.3 143.1 135.9 129.6 122.4 115.2
100 210.0 202.0 193.0 184.0 175.0 167.0 159.0 151.0 144.0 136.0 128.0
Figure 48: C3H8 (POX) – System Load versus Part Load.
89
Table 44: C3H8 (POX) – Fuel Utilization.
Fuel Utilization ( – C3H8 (POX)
Load
(%)
Altitude (ft) 0E+0 2E+3 4E+3 6E+3 8E+3 10E+3 12E+3 14E+3 16E+3 18E+3 20E+3
10 0.190 0.192 0.193 0.193 0.194 0.195 0.196 0.197 0.198 0.198 0.198 20 0.321 0.323 0.325 0.325 0.327 0.328 0.329 0.330 0.332 0.332 0.332 30 0.417 0.419 0.421 0.422 0.423 0.425 0.426 0.427 0.426 0.415 0.405 40 0.490 0.492 0.494 0.494 0.490 0.482 0.480 0.470 0.465 0.456 0.451 50 0.514 0.515 0.513 0.509 0.505 0.502 0.498 0.493 0.487 0.482 0.475 60 0.522 0.522 0.519 0.517 0.516 0.513 0.510 0.504 0.502 0.499 0.493 70 0.526 0.524 0.524 0.522 0.521 0.519 0.517 0.515 0.513 0.509 0.505 80 0.527 0.527 0.525 0.525 0.524 0.524 0.522 0.520 0.518 0.516 0.514 90 0.527 0.527 0.527 0.527 0.527 0.527 0.526 0.525 0.524 0.523 0.522
100 0.530 0.532 0.532 0.532 0.532 0.532 0.532 0.532 0.532 0.532 0.531
Figure 49: C3H8 (POX) – Fuel Utilization versus Part Load.
90
Table 45: C3H8 (POX) – Turbine Inlet Temperature.
Turbine Inlet Temperature (K) – C3H8 (POX)
Load
(%)
Altitude (ft) 0E+0 2E+3 4E+3 6E+3 8E+3 10E+3 12E+3 14E+3 16E+3 18E+3 20E+3
10 1085 1086 1087 1088 1088 1089 1090 1090 1091 1092 1092 20 1087 1087 1088 1089 1089 1090 1091 1091 1092 1093 1093 30 1089 1090 1090 1091 1091 1092 1092 1093 1093 1093 1093 40 1092 1092 1093 1093 1093 1093 1093 1093 1093 1093 1093 50 1093 1093 1093 1093 1093 1093 1093 1093 1093 1093 1093 60 1093 1093 1093 1093 1093 1093 1093 1093 1093 1093 1093 70 1093 1093 1093 1093 1093 1093 1093 1093 1093 1093 1093 80 1093 1093 1093 1093 1093 1093 1093 1093 1093 1093 1093 90 1093 1093 1093 1093 1093 1093 1093 1093 1093 1093 1093
100 1093 1093 1093 1093 1093 1093 1093 1093 1093 1093 1093
Figure 50: C3H8 (POX) – Turbine Inlet Temperature versus Part Load.
91
Table 46: C3H8 (POX) – Gas Turbine Shaft Speed.
Shaft Speed (kRPM) – C3H8 (POX)
Load
(%)
Altitude (ft) 0E+0 2E+3 4E+3 6E+3 8E+3 10E+3 12E+3 14E+3 16E+3 18E+3 20E+3
10 55.0 55.0 55.0 55.0 55.0 55.0 55.0 55.0 55.0 55.0 55.0 20 55.0 55.0 55.0 55.0 55.0 55.0 55.0 55.0 55.0 55.0 55.0 30 55.0 55.0 55.0 55.0 55.0 55.0 55.0 55.0 56.3 60.1 63.8 40 55.0 55.0 55.0 55.3 57.2 60.1 61.9 65.8 68.9 71.9 73.4 50 66.1 67.2 68.9 70.9 73.2 74.5 76.0 77.7 80.1 81.6 83.4 60 81.3 82.1 83.5 84.2 84.9 86.2 87.4 89.0 90.3 91.0 92.2 70 94.1 95.2 95.5 95.9 96.3 96.9 97.7 98.1 98.8 99.4 99.8 80 105.1 105.3 105.7 105.4 105.6 105.6 105.9 106.3 107.1 107.3 107.4 90 115.1 115.3 115.3 115.0 114.9 114.8 114.9 115.0 115.6 115.5 115.1
100 125.0 125.0 125.0 125.0 125.0 125.0 125.0 125.0 125.0 125.0 125.0
Figure 51: C3H8 (POX) – Gas Turbine Shaft Speed versus Part Load.
92
Table 47: C3H8 (POX) – Compressor Mass Flow Rate.
Compressor Mass Flow Rate (kg/s) – C3H8 (POX)
Load
(%)
Altitude (ft) 0E+0 2E+3 4E+3 6E+3 8E+3 10E+3 12E+3 14E+3 16E+3 18E+3 20E+3
10 0.043 0.040 0.038 0.036 0.033 0.031 0.029 0.027 0.026 0.024 0.022 20 0.043 0.041 0.038 0.036 0.034 0.032 0.030 0.028 0.026 0.024 0.023 30 0.043 0.041 0.039 0.036 0.034 0.032 0.030 0.028 0.027 0.026 0.026 40 0.044 0.041 0.039 0.037 0.035 0.034 0.033 0.032 0.031 0.030 0.029 50 0.051 0.048 0.046 0.044 0.043 0.041 0.039 0.038 0.037 0.035 0.034 60 0.061 0.058 0.056 0.053 0.050 0.048 0.046 0.044 0.042 0.040 0.039 70 0.072 0.069 0.066 0.062 0.059 0.056 0.054 0.051 0.049 0.046 0.044 80 0.085 0.081 0.077 0.073 0.069 0.065 0.062 0.059 0.056 0.053 0.050 90 0.099 0.094 0.089 0.084 0.079 0.075 0.071 0.067 0.064 0.060 0.056
100 0.113 0.107 0.101 0.095 0.090 0.085 0.080 0.075 0.071 0.066 0.062
Figure 52: C3H8 (POX) – Compressor Mass Flow Rate versus Part Load.
93
Table 48: C3H8 (POX) – Solid Oxide Fuel Cell Voltage.
SOFC Voltage (V) – C3H8 (POX)
Load
(%)
Altitude (ft) 0E+0 2E+3 4E+3 6E+3 8E+3 10E+3 12E+3 14E+3 16E+3 18E+3 20E+3
10 0.915 0.915 0.915 0.915 0.915 0.914 0.914 0.913 0.912 0.912 0.912 20 0.850 0.851 0.853 0.855 0.857 0.858 0.859 0.860 0.861 0.862 0.864 30 0.790 0.793 0.797 0.801 0.804 0.807 0.810 0.813 0.816 0.821 0.826 40 0.735 0.740 0.745 0.750 0.756 0.763 0.768 0.775 0.780 0.787 0.793 50 0.690 0.696 0.704 0.712 0.720 0.727 0.734 0.741 0.748 0.755 0.763 60 0.650 0.658 0.667 0.676 0.685 0.693 0.702 0.711 0.718 0.726 0.736 70 0.613 0.622 0.632 0.642 0.653 0.662 0.671 0.681 0.689 0.699 0.709 80 0.578 0.588 0.599 0.610 0.622 0.632 0.642 0.653 0.663 0.674 0.685 90 0.545 0.556 0.568 0.580 0.592 0.603 0.615 0.626 0.637 0.649 0.661
100 0.514 0.525 0.538 0.551 0.564 0.576 0.588 0.601 0.612 0.624 0.638
Figure 53: C3H8 (POX) – Solid Oxide Fuel Cell Voltage versus Part Load.
94
Table 49: C3H8 (POX) – Solid Oxide Fuel Cell Power.
SOFC Power (kW) – C3H8 (POX)
Load
(%)
Altitude (ft) 0E+0 2E+3 4E+3 6E+3 8E+3 10E+3 12E+3 14E+3 16E+3 18E+3 20E+3
10 3.46 3.33 3.18 3.03 2.88 2.75 2.61 2.48 2.37 2.23 2.10 20 6.43 6.19 5.93 5.66 5.40 5.16 4.92 4.68 4.46 4.22 3.98 30 8.96 8.65 8.30 7.95 7.60 7.28 6.95 6.63 6.34 6.03 5.71 40 11.12 10.76 10.35 9.94 9.53 9.17 8.79 8.42 8.09 7.70 7.30 50 13.05 12.66 12.22 11.79 11.34 10.92 10.50 10.07 9.69 9.25 8.79 60 14.75 14.35 13.90 13.43 12.95 12.50 12.05 11.59 11.16 10.67 10.17 70 16.22 15.83 15.37 14.89 14.39 13.93 13.45 12.95 12.51 11.98 11.44 80 17.48 17.09 16.65 16.17 15.67 15.19 14.71 14.20 13.74 13.19 12.62 90 18.55 18.19 17.75 17.29 16.79 16.32 15.84 15.32 14.85 14.29 13.70
100 19.43 19.08 18.68 18.24 17.77 17.32 16.84 16.33 15.85 15.29 14.69
Figure 54: C3H8 (POX) – Solid Oxide Fuel Cell Power versus Part Load.
95
Table 50: C3H8 (POX) – Gas Turbine Power.
GT Power (kW) – C3H8 (POX)
Load
(%)
Altitude (ft) 0E+0 2E+3 4E+3 6E+3 8E+3 10E+3 12E+3 14E+3 16E+3 18E+3 20E+3
10 1.73 1.71 1.68 1.65 1.60 1.56 1.52 1.48 1.43 1.38 1.34 20 1.84 1.82 1.78 1.74 1.69 1.65 1.61 1.56 1.51 1.46 1.40 30 1.96 1.93 1.88 1.84 1.79 1.74 1.69 1.64 1.61 1.65 1.67 40 2.08 2.04 1.99 1.95 1.94 1.97 1.95 1.99 2.00 2.02 2.00 50 2.50 2.49 2.48 2.47 2.46 2.45 2.45 2.44 2.46 2.44 2.43 60 3.10 3.09 3.08 3.06 3.01 3.00 2.98 2.98 2.96 2.91 2.88 70 3.73 3.74 3.70 3.67 3.62 3.59 3.56 3.51 3.48 3.43 3.37 80 4.34 4.35 4.33 4.28 4.23 4.18 4.13 4.08 4.04 3.97 3.87 90 4.89 4.91 4.89 4.85 4.79 4.75 4.70 4.63 4.58 4.48 4.36
100 5.25 5.30 5.31 5.29 5.25 5.22 5.17 5.09 5.03 4.92 4.80
Figure 55: C3H8 (POX) – Gas Turbine Power versus Part Load.
96
Table 51: JP8 (POX) – System Load.
Part Load (A) Calculations – JP8 (POX)
Load
(%)
Altitude (ft) 0E+0 2E+3 4E+3 6E+3 8E+3 10E+3 12E+3 14E+3 16E+3 18E+3 20E+3
10 21.2 20.2 19.3 18.5 17.6 16.8 16.0 15.2 14.4 13.6 12.9 20 42.4 40.4 38.6 37.0 35.2 33.6 32.0 30.4 28.8 27.2 25.8 30 63.6 60.6 57.9 55.5 52.8 50.4 48.0 45.6 43.2 40.8 38.7 40 84.8 80.8 77.2 74.0 70.4 67.2 64.0 60.8 57.6 54.4 51.6 50 106.0 101.0 96.5 92.5 88.0 84.0 80.0 76.0 72.0 68.0 64.5 60 127.2 121.2 115.8 111.0 105.6 100.8 96.0 91.2 86.4 81.6 77.4 70 148.4 141.4 135.1 129.5 123.2 117.6 112.0 106.4 100.8 95.2 90.3 80 169.6 161.6 154.4 148.0 140.8 134.4 128.0 121.6 115.2 108.8 103.2 90 190.8 181.8 173.7 166.5 158.4 151.2 144.0 136.8 129.6 122.4 116.1
100 212.0 202.0 193.0 185.0 176.0 168.0 160.0 152.0 144.0 136.0 129.0
Figure 56: JP8 (POX) – System Load versus Part Load.
97
Table 52: JP8 (POX) - Fuel Utilization.
Fuel Utilization ( – JP8 (POX)
Load
(%)
Altitude (ft) 0E+0 2E+3 4E+3 6E+3 8E+3 10E+3 12E+3 14E+3 16E+3 18E+3 20E+3
10 0.193 0.193 0.194 0.195 0.196 0.197 0.198 0.198 0.199 0.199 0.2 20 0.325 0.325 0.326 0.328 0.33 0.331 0.332 0.333 0.333 0.334 0.335 30 0.421 0.421 0.423 0.425 0.427 0.428 0.429 0.431 0.428 0.415 0.41 40 0.495 0.494 0.496 0.496 0.492 0.485 0.483 0.475 0.468 0.461 0.452 50 0.521 0.516 0.516 0.514 0.509 0.505 0.482 0.5 0.492 0.486 0.48 60 0.524 0.523 0.523 0.522 0.52 0.514 0.499 0.507 0.507 0.502 0.494 70 0.526 0.525 0.525 0.525 0.525 0.524 0.522 0.52 0.516 0.513 0.511 80 0.529 0.527 0.527 0.527 0.527 0.527 0.527 0.526 0.524 0.52 0.517 90 0.53 0.53 0.53 0.53 0.53 0.529 0.529 0.528 0.528 0.528 0.526
100 0.536 0.535 0.535 0.536 0.536 0.536 0.536 0.536 0.536 0.536 0.536
Figure 57: JP8 (POX) – Fuel Utilization versus Part Load.
98
Table 53: JP8 (POX) – Turbine Inlet Temperature.
Turbine Inlet Temperature (K) – JP8 (POX)
Load
(%)
Altitude (ft) 0E+0 2E+3 4E+3 6E+3 8E+3 10E+3 12E+3 14E+3 16E+3 18E+3 20E+3
10 1085 1086 1087 1087 1088 1089 1090 1090 1091 1092 1092 20 1087 1087 1088 1089 1089 1090 1091 1091 1092 1092 1093 30 1089 1089 1090 1091 1091 1092 1092 1093 1093 1093 1093 40 1092 1092 1093 1093 1093 1093 1093 1093 1093 1093 1093 50 1093 1093 1093 1093 1093 1093 1093 1093 1093 1093 1093 60 1093 1093 1093 1093 1093 1093 1093 1093 1093 1093 1093 70 1093 1093 1093 1093 1093 1093 1093 1093 1093 1093 1093 80 1093 1093 1093 1093 1093 1093 1093 1093 1093 1093 1093 90 1093 1093 1093 1093 1093 1093 1093 1093 1093 1093 1093
100 1093 1093 1093 1093 1093 1093 1093 1093 1093 1093 1093
Figure 58: JP8 (POX) – Turbine Inlet Temperature versus Part Load.
99
Table 54: JP8 (POX) – Gas Turbine Shaft Speed.
Shaft Speed (kRPM) – JP8 (POX)
Load
(%)
Altitude (ft) 0E+0 2E+3 4E+3 6E+3 8E+3 10E+3 12E+3 14E+3 16E+3 18E+3 20E+3
10 55.0 55.0 55.0 55.0 55.0 55.0 55.0 55.0 55.0 55.0 55.0 20 55.0 55.0 55.0 55.0 55.0 55.0 55.0 55.0 55.0 55.0 55.0 30 55.0 55.0 55.0 55.0 55.0 55.0 55.0 55.0 56.1 60.4 63.4 40 55.0 55.0 55.0 55.6 57.5 60.2 62.1 65.4 68.5 71.2 74.0 50 65.6 67.3 68.5 70.5 73.1 74.6 80.2 77.1 79.3 81.1 83.3 60 82.1 82.3 82.9 83.9 84.9 86.8 90.5 89.3 89.6 90.8 92.8 70 95.4 95.3 95.6 96.1 96.4 96.7 97.6 98.0 98.6 99.0 99.6 80 105.9 105.7 105.7 105.8 105.8 105.8 105.8 106.0 106.2 106.9 107.7 90 115.8 115.1 115.1 115.2 115.1 115.3 115.3 115.4 115.1 114.8 115.4
100 125.0 125.0 125.0 125.0 125.0 125.0 125.0 125.0 125.0 125.0 125.0
Figure 59: JP8 (POX) – Gas Turbine Shaft Speed versus Part Load.
100
Table 55: JP8 (POX) – Compressor Mass Flow Rate.
Compressor Mass Flow Rate (kg/s) – JP8 (POX)
Load
(%)
Altitude (ft) 0E+0 2E+3 4E+3 6E+3 8E+3 10E+3 12E+3 14E+3 16E+3 18E+3 20E+3
10 0.043 0.041 0.038 0.036 0.034 0.032 0.030 0.028 0.026 0.024 0.023 20 0.043 0.041 0.039 0.036 0.034 0.032 0.030 0.028 0.026 0.025 0.023 30 0.044 0.041 0.039 0.037 0.034 0.032 0.030 0.028 0.027 0.027 0.026 40 0.044 0.042 0.039 0.037 0.036 0.035 0.033 0.033 0.031 0.030 0.030 50 0.051 0.049 0.047 0.045 0.043 0.041 0.042 0.038 0.037 0.035 0.034 60 0.062 0.059 0.056 0.053 0.051 0.049 0.049 0.045 0.043 0.041 0.039 70 0.074 0.070 0.067 0.063 0.060 0.057 0.054 0.052 0.049 0.047 0.044 80 0.087 0.082 0.078 0.074 0.070 0.066 0.063 0.059 0.056 0.053 0.051 90 0.101 0.095 0.090 0.085 0.080 0.076 0.072 0.068 0.064 0.060 0.057
100 0.114 0.108 0.102 0.096 0.091 0.086 0.081 0.076 0.071 0.067 0.063
Figure 60: JP8 (POX) – Compressor Mass Flow Rate versus Part Load.
101
Table 56: JP8 (POX) – Solid Oxide Fuel Cell Voltage.
SOFC Voltage (V) – JP8 (POX)
Load
(%)
Altitude (ft) 0E+0 2E+3 4E+3 6E+3 8E+3 10E+3 12E+3 14E+3 16E+3 18E+3 20E+3
10 0.911 0.911 0.911 0.911 0.911 0.910 0.910 0.909 0.909 0.908 0.908 20 0.846 0.848 0.850 0.851 0.853 0.854 0.856 0.857 0.858 0.859 0.860 30 0.786 0.791 0.794 0.797 0.800 0.803 0.806 0.809 0.813 0.818 0.822 40 0.730 0.737 0.742 0.747 0.753 0.759 0.764 0.771 0.777 0.784 0.789 50 0.685 0.694 0.701 0.708 0.716 0.723 0.734 0.737 0.745 0.753 0.759 60 0.646 0.656 0.664 0.672 0.681 0.690 0.701 0.707 0.715 0.724 0.732 70 0.609 0.620 0.630 0.638 0.648 0.658 0.667 0.677 0.687 0.696 0.705 80 0.573 0.586 0.597 0.606 0.618 0.628 0.638 0.648 0.659 0.671 0.681 90 0.540 0.553 0.565 0.576 0.588 0.599 0.611 0.622 0.634 0.645 0.656
100 0.508 0.522 0.535 0.546 0.560 0.572 0.584 0.596 0.609 0.622 0.633
Figure 61: JP8 (POX) – Solid Oxide Fuel Cell Voltage versus Part Load.
102
Table 57: JP8 (POX) – Solid Oxide Fuel Cell Power.
SOFC Power (kW) – JP8 (POX)
Load
(%)
Altitude (ft) 0E+0 2E+3 4E+3 6E+3 8E+3 10E+3 12E+3 14E+3 16E+3 18E+3 20E+3
10 3.48 3.31 3.17 3.03 2.88 2.75 2.62 2.49 2.36 2.22 2.11 20 6.45 6.17 5.91 5.67 5.40 5.17 4.93 4.69 4.45 4.21 3.99 30 9.00 8.62 8.28 7.96 7.61 7.29 6.97 6.64 6.32 6.01 5.73 40 11.15 10.72 10.31 9.95 9.54 9.18 8.81 8.44 8.06 7.67 7.33 50 13.07 12.62 12.18 11.78 11.34 10.93 10.57 10.08 9.65 9.21 8.82 60 14.79 14.30 13.84 13.42 12.94 12.52 12.11 11.60 11.12 10.63 10.20 70 16.26 15.78 15.31 14.88 14.38 13.92 13.45 12.96 12.46 11.93 11.46 80 17.50 17.04 16.58 16.16 15.65 15.19 14.70 14.19 13.67 13.13 12.64 90 18.54 18.10 17.67 17.26 16.77 16.32 15.83 15.32 14.79 14.22 13.71
100 19.39 18.98 18.59 18.20 17.73 17.29 16.82 16.31 15.78 15.22 14.69
Figure 62: JP8 (POX) – Solid Oxide Fuel Cell Power versus Part Load.
103
Table 58: JP8 (POX) – Gas Turbine Power.
GT Power (kW) – JP8 (POX)
Load
(%)
Altitude (ft) 0E+0 2E+3 4E+3 6E+3 8E+3 10E+3 12E+3 14E+3 16E+3 18E+3 20E+3
10 1.77 1.74 1.71 1.68 1.63 1.59 1.55 1.51 1.46 1.41 1.36 20 1.89 1.86 1.82 1.78 1.73 1.69 1.64 1.59 1.54 1.48 1.43 30 2.01 1.97 1.93 1.89 1.83 1.78 1.73 1.68 1.65 1.69 1.70 40 2.14 2.10 2.05 2.01 2.00 2.02 2.00 2.03 2.04 2.04 2.07 50 2.57 2.57 2.53 2.53 2.53 2.53 2.69 2.48 2.49 2.48 2.48 60 3.23 3.19 3.15 3.13 3.10 3.11 3.22 3.07 3.00 2.97 2.99 70 3.91 3.86 3.82 3.79 3.73 3.69 3.65 3.60 3.56 3.50 3.44 80 4.53 4.50 4.47 4.44 4.37 4.31 4.25 4.18 4.11 4.05 4.00 90 5.09 5.06 5.04 5.02 4.96 4.92 4.85 4.78 4.68 4.57 4.50
100 5.46 5.47 5.48 5.47 5.43 5.39 5.33 5.25 5.16 5.04 4.94
Figure 63: JP8 (POX) – Gas Turbine Power versus Part Load.
104
Table 59: CH4 (IR) – Part Load System Efficiency.
Part Load System Efficiency – CH4 (IR)
Load
(%)
Altitude (ft) 0E+0 2E+3 4E+3 6E+3 8E+3 10E+3 12E+3 14E+3 16E+3 18E+3 20E+3
10 0.270 0.271 0.275 0.278 0.281 0.285 0.288 0.291 0.294 0.296 0.299 20 0.362 0.364 0.368 0.371 0.376 0.379 0.382 0.386 0.389 0.392 0.395 30 0.410 0.413 0.418 0.422 0.426 0.431 0.434 0.439 0.442 0.443 0.441 40 0.432 0.437 0.442 0.447 0.452 0.457 0.458 0.459 0.460 0.460 0.461 50 0.430 0.436 0.441 0.445 0.450 0.453 0.457 0.460 0.463 0.466 0.468 60 0.413 0.421 0.428 0.433 0.439 0.445 0.449 0.455 0.460 0.464 0.469 70 0.395 0.404 0.412 0.419 0.427 0.433 0.440 0.446 0.453 0.459 0.464 80 0.377 0.387 0.396 0.404 0.413 0.421 0.429 0.436 0.444 0.451 0.459 90 0.358 0.369 0.379 0.388 0.398 0.407 0.416 0.425 0.434 0.443 0.451
100 0.339 0.351 0.362 0.372 0.383 0.393 0.403 0.413 0.423 0.433 0.443
Table 60: JP8 (SR) – Part Load System Efficency.
Part Load System Efficiency – JP8 (SR)
Load
(%)
Altitude (ft) 0E+0 2E+3 4E+3 6E+3 8E+3 10E+3 12E+3 14E+3 16E+3 18E+3 20E+3
10 0.263 0.262 0.265 0.270 0.273 0.276 0.279 0.283 0.285 0.287 0.290 20 0.349 0.352 0.355 0.359 0.364 0.367 0.371 0.374 0.377 0.379 0.383 30 0.397 0.400 0.404 0.409 0.414 0.417 0.421 0.426 0.429 0.426 0.425 40 0.419 0.424 0.429 0.434 0.438 0.440 0.442 0.442 0.442 0.445 0.444 50 0.417 0.421 0.425 0.429 0.433 0.437 0.441 0.444 0.447 0.450 0.453 60 0.402 0.407 0.412 0.418 0.424 0.429 0.435 0.439 0.445 0.450 0.454 70 0.385 0.391 0.397 0.404 0.412 0.419 0.426 0.433 0.439 0.444 0.451 80 0.367 0.375 0.382 0.390 0.399 0.407 0.415 0.423 0.431 0.439 0.446 90 0.349 0.358 0.367 0.376 0.386 0.395 0.403 0.412 0.422 0.429 0.438
100 0.331 0.342 0.352 0.362 0.373 0.383 0.393 0.403 0.413 0.422 0.432
105
Table 61: H2 – Part Load System Efficiecy.
Part Load System Efficiency – H2
Load
(%)
Altitude (ft) 0E+0 2E+3 4E+3 6E+3 8E+3 10E+3 12E+3 14E+3 16E+3 18E+3 20E+3
10 0.209 0.212 0.214 0.217 0.220 0.223 0.225 0.228 0.230 0.232 0.235 20 0.282 0.284 0.288 0.291 0.295 0.297 0.300 0.303 0.306 0.308 0.308 30 0.320 0.324 0.328 0.331 0.336 0.339 0.342 0.342 0.341 0.340 0.340 40 0.337 0.340 0.343 0.344 0.346 0.348 0.350 0.351 0.352 0.353 0.354 50 0.327 0.330 0.335 0.338 0.342 0.345 0.348 0.351 0.353 0.356 0.358 60 0.313 0.318 0.324 0.329 0.333 0.338 0.342 0.346 0.350 0.355 0.359 70 0.298 0.305 0.311 0.317 0.324 0.329 0.335 0.340 0.345 0.350 0.356 80 0.284 0.291 0.298 0.305 0.312 0.319 0.326 0.332 0.338 0.344 0.350 90 0.269 0.277 0.285 0.293 0.300 0.308 0.316 0.323 0.330 0.338 0.345
100 0.265 0.273 0.281 0.289 0.297 0.305 0.313 0.321 0.329 0.337 0.345
Table 62: CH4 (POX) – Part Load System Efficiency.
Part Load System Efficiency – CH4 (POX)
Load
(%)
Altitude (ft) 0E+0 2E+3 4E+3 6E+3 8E+3 10E+3 12E+3 14E+3 16E+3 18E+3 20E+3
10 0.187 0.190 0.192 0.195 0.198 0.200 0.203 0.205 0.207 0.209 0.211 20 0.253 0.256 0.258 0.261 0.264 0.267 0.270 0.273 0.274 0.277 0.278 30 0.289 0.292 0.295 0.299 0.302 0.306 0.308 0.311 0.311 0.311 0.310 40 0.307 0.311 0.315 0.317 0.319 0.320 0.321 0.323 0.322 0.323 0.325 50 0.304 0.307 0.311 0.314 0.317 0.319 0.322 0.325 0.327 0.329 0.331 60 0.293 0.298 0.303 0.307 0.311 0.315 0.319 0.322 0.326 0.330 0.332 70 0.282 0.288 0.294 0.299 0.304 0.309 0.313 0.318 0.323 0.327 0.331 80 0.270 0.276 0.283 0.289 0.295 0.301 0.307 0.312 0.318 0.323 0.328 90 0.258 0.265 0.272 0.279 0.286 0.292 0.299 0.306 0.312 0.318 0.324
100 0.247 0.255 0.263 0.270 0.278 0.285 0.292 0.299 0.306 0.314 0.321
106
Table 63: C3H8 (POX) – Part Load System Efficiency.
Part Load System Efficiency – C3H8 (POX)
Load
(%)
Altitude (ft) 0E+0 2E+3 4E+3 6E+3 8E+3 10E+3 12E+3 14E+3 16E+3 18E+3 20E+3
10 0.173 0.176 0.179 0.181 0.183 0.185 0.188 0.190 0.192 0.194 0.195 20 0.233 0.236 0.239 0.241 0.244 0.246 0.248 0.251 0.253 0.255 0.257 30 0.266 0.269 0.273 0.276 0.278 0.282 0.284 0.287 0.289 0.287 0.286 40 0.283 0.287 0.291 0.294 0.296 0.296 0.298 0.298 0.300 0.300 0.302 50 0.280 0.284 0.288 0.290 0.293 0.296 0.299 0.301 0.302 0.305 0.307 60 0.272 0.276 0.280 0.284 0.289 0.292 0.296 0.298 0.302 0.306 0.308 70 0.263 0.267 0.272 0.277 0.282 0.286 0.291 0.295 0.299 0.303 0.307 80 0.252 0.257 0.263 0.268 0.274 0.280 0.285 0.290 0.294 0.299 0.305 90 0.241 0.246 0.253 0.259 0.266 0.272 0.278 0.284 0.289 0.295 0.301
100 0.229 0.236 0.243 0.250 0.258 0.264 0.271 0.278 0.284 0.291 0.298
Table 64: JP8 (POX) – Part Load System Efficiency.
Part Load System Efficiency – JP8 (POX)
Load
(%)
Altitude (ft) 0E+0 2E+3 4E+3 6E+3 8E+3 10E+3 12E+3 14E+3 16E+3 18E+3 20E+3
10 0.170 0.172 0.175 0.177 0.179 0.182 0.184 0.185 0.188 0.189 0.192 20 0.228 0.230 0.233 0.235 0.238 0.241 0.243 0.245 0.247 0.249 0.251 30 0.260 0.262 0.266 0.269 0.272 0.275 0.277 0.280 0.281 0.279 0.280 40 0.276 0.279 0.283 0.286 0.288 0.288 0.291 0.291 0.292 0.293 0.294 50 0.274 0.276 0.280 0.283 0.286 0.288 0.285 0.295 0.296 0.298 0.300 60 0.265 0.269 0.274 0.278 0.282 0.284 0.284 0.291 0.295 0.298 0.300 70 0.255 0.260 0.265 0.270 0.275 0.280 0.284 0.288 0.292 0.296 0.301 80 0.245 0.250 0.256 0.261 0.267 0.273 0.278 0.283 0.288 0.293 0.297 90 0.234 0.241 0.247 0.253 0.259 0.265 0.271 0.277 0.283 0.289 0.294
100 0.224 0.231 0.238 0.244 0.251 0.258 0.264 0.271 0.278 0.285 0.291
107
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